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A first idea of quantum field theory -- Scattering
https://ncatlab.org/nlab/source/A+first+idea+of+quantum+field+theory+--+Scattering
see _[[A first idea of quantum field theory -- Interacting quantum fields]]_
A first idea of quantum field theory -- Spacetime
https://ncatlab.org/nlab/source/A+first+idea+of+quantum+field+theory+--+Spacetime
## Spacetime {#Spacetime} [[relativistic field theory|Relativistic field theory]] takes place on _[[spacetime]]_. The concept of [[spacetime]] makes sense for every [[dimension]] $p+1$ with $p \in \mathbb{N}$. The [[observable universe]] has macroscopic dimension $3+1$, but [[quantum field theory]] generall...
A first idea of quantum field theory -- Symmetries
https://ncatlab.org/nlab/source/A+first+idea+of+quantum+field+theory+--+Symmetries
## Symmetries {#Symmetries} In this chapter we discuss these topics: * _[Infinitesimal symmetries of the Lagrangian density](#InfinitesimalSymmetriesOfTheLagrangianDensity)_ * _[Infinitesimal symmetries of the presymplectic potential current](#InfinitesimalSymmetriesOfThePresymplecticPotentialCurrent)_ ...
A first idea of quantum field theory > history
https://ncatlab.org/nlab/source/A+first+idea+of+quantum+field+theory+%3E+history
see _[[geometry of physics -- A first idea of quantum field theory]]_
A History of Western Philosophy
https://ncatlab.org/nlab/source/A+History+of+Western+Philosophy
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ### Context #### Philosophy +-- {: .hide} [[!include philosophy - contents]] =-- =-- =-- This page collects material related to * [[Bertrand Russell]], _A History of Western Philosophy_ 1945 on the history of [[philosophy]]. ## Chapter 22 -- Hegel ...
A mechanization of the Blakers-Massey connectivity theorem in Homotopy Type Theory
https://ncatlab.org/nlab/source/A+mechanization+of+the+Blakers-Massey+connectivity+theorem+in+Homotopy+Type+Theory
* [[Kuen-Bang Hou (Favonia)]], [[Eric Finster]], [[Dan Licata]], [[Peter LeFanu Lumsdaine]]: **A mechanization of the Blakers-Massey connectivity theorem in Homotopy Type Theory** LICS'16 (2016) 565–574 [arXiv:1605.03227](https://arxiv.org/abs/1605.03227) [doi:10.1145/2933575.2934545](https://doi....
A Not-So-Nice Submanifold
https://ncatlab.org/nlab/source/A+Not-So-Nice+Submanifold
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Mapping space +--{: .hide} [[!include mapping space - contents]] =-- =-- =-- ## Idea ## As shown in [[evaluation fibration of mapping spaces]] and [[tubular neighbourhoods of mapping spaces]], if we carve out a submanifold of a mapping spa...
A Polarized View of String Topology
https://ncatlab.org/nlab/source/A+Polarized+View+of+String+Topology
This entry is about the article * [[Ralph Cohen]], [[Veronique Godin]], _A polarized view of string topology_, In: [[Graeme Segal]], [[Ulrike Tillmann]] (eds.) _Topology, Geometry and Quantum Field Theory_, LMS, Lecture Notes Series 308, 2004 [arXiv:math/0303003](http://arxiv.org...
A pseudo metric space, i.e. a set with a metric where the distance between two distinct points can also be 0, need not be Haussdorf
https://ncatlab.org/nlab/source/A+pseudo+metric+space%2C+i.e.+a+set+with+a+metric+where+the+distance+between+two+distinct+points+can+also+be+0%2C+need+not+be+Haussdorf
>This is not really the place to ask what seems to be a question. You could ask us on the n-forum or better on [math.stackexchange](http://math.stackexchange.com/) for questions that are high level but not research questions.
a Serre fibration between CW-complexes is a Hurewicz fibration
https://ncatlab.org/nlab/source/a+Serre+fibration+between+CW-complexes+is+a+Hurewicz+fibration
## Statement \begin{theorem} Let $X$ and $Y$ be [[CW-complexes]] and $f:X\to Y$ a [[Serre fibration]]. Then $f$ is in fact a [[Hurewicz fibration]] (at least in a [[convenient category of spaces]]). \end{theorem} ## References This was originally proven in * Mark Steinberger and James West, *Covering hom...
A string diagram calculus for predicate logic
https://ncatlab.org/nlab/source/A+string+diagram+calculus+for+predicate+logic
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Monoidal categories +--{: .hide} [[!include monoidal categories - contents]] =-- =-- =-- This page is to provide links related to the text * [[Geraldine Brady]], [[Todd Trimble]], _A string diagram calculus for predicate logic and C. S...
A study in derived algebraic geometry
https://ncatlab.org/nlab/source/A+study+in+derived+algebraic+geometry
This entry is about the book (in progress) * [[D. Gaitsgory]], [[N. Rozenblyum]], _A study in derived algebraic geometry_, [web](http://www.math.harvard.edu/~gaitsgde/GL/). It develops some aspects of the theory of [[derived algebraic geometry]] with the [[categorical geometric Langlands conjecture]] in mind. ## See...
A Survey of Cohomological Physics
https://ncatlab.org/nlab/source/A+Survey+of+Cohomological+Physics
* [[Jim Stasheff]], _[[StasheffCohomPhysicsSurvey.pdf:file]]_, 2009 See also * {#Stasheff16} [[Jim Stasheff]], _Higher homotopy structures, then and now_, talk at _[Opening workshop](https://www.mpim-bonn.mpg.de/node/6356)_ of _[Higher Structures in Geometry and Physics](https://www.mpim-bonn.mpg.de/node/5883)_, MP...
A Survey of Elliptic Cohomology
https://ncatlab.org/nlab/source/A+Survey+of+Elliptic+Cohomology
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Cohomology +--{: .hide} [[!include cohomology - contents]] =-- #### Higher geometry +--{: .hide} [[!include higher geometry - contents]] =-- #### Higher algebra +--{: .hide} [[!include higher algebra - contents]] =-- =-- ...
A Survey of Elliptic Cohomology - A-equivariant cohomology
https://ncatlab.org/nlab/source/A+Survey+of+Elliptic+Cohomology+-+A-equivariant+cohomology
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Cohomology +--{: .hide} [[!include cohomology - contents]] =-- #### Higher algebra +--{: .hide} [[!include higher algebra - contents]] =-- =-- =-- +-- {: .standout} This is a sub-entry of * [[A Survey of Elliptic Cohomology]] see the...
A Survey of Elliptic Cohomology - cohomology theories
https://ncatlab.org/nlab/source/A+Survey+of+Elliptic+Cohomology+-+cohomology+theories
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Cohomology +--{: .hide} [[!include cohomology - contents]] =-- #### Higher geometry +--{: .hide} [[!include higher geometry - contents]] =-- #### Higher algebra +--{: .hide} [[!include higher algebra - contents]] =-- =-- ...
A Survey of Elliptic Cohomology - compactifying the derived moduli stack
https://ncatlab.org/nlab/source/A+Survey+of+Elliptic+Cohomology+-+compactifying+the+derived+moduli+stack
[[!redirects A Survey of Elliptic Cohomology - compactifying the derived moduli space]] <div class="rightHandSide toc"> [[!include higher algebra - contents]] </div> >**Abstract** We sketch how to compactify $M^{Der}$ such that the underlying scheme is the Deligne-Mumford compactification of $M_{1,1}$. +-- {: ....
A Survey of Elliptic Cohomology - derived group schemes and (pre-)orientations
https://ncatlab.org/nlab/source/A+Survey+of+Elliptic+Cohomology+-+derived+group+schemes+and+%28pre-%29orientations
<div class="rightHandSide toc"> [[!include cohomology - contents]] *** [[!include higher algebra - contents]] </div> +-- {: .standout} This is a sub-entry of * [[A Survey of Elliptic Cohomology]] see there for background and context. This entry contains a basic introduction to derived [[group scheme]]s and ...
A Survey of Elliptic Cohomology - descent ss and coefficients
https://ncatlab.org/nlab/source/A+Survey+of+Elliptic+Cohomology+-+descent+ss+and+coefficients
[[!redirects A Survey of Elliptic Cohomology - compactifying the derived moduli space]] +-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Higher algebra +--{: .hide} [[!include higher algebra - contents]] =-- =-- =-- >**Abstract** This entry discusses the [[descent spectral sequence]] a...
A Survey of Elliptic Cohomology - E-infinity rings and derived schemes
https://ncatlab.org/nlab/source/A+Survey+of+Elliptic+Cohomology+-+E-infinity+rings+and+derived+schemes
<div class="rightHandSide toc"> [[!include cohomology - contents]] *** [[!include higher algebra - contents]] </div> +-- {: .standout} This is a sub-entry of * [[A Survey of Elliptic Cohomology]] see there for background and context. This entry discusses the algebraic/homotopy theoretic prerequisites for [[d...
A Survey of Elliptic Cohomology - elliptic curves
https://ncatlab.org/nlab/source/A+Survey+of+Elliptic+Cohomology+-+elliptic+curves
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Cohomology +--{: .hide} [[!include cohomology - contents]] =-- #### Higher geometry +--{: .hide} [[!include higher geometry - contents]] =-- =-- =-- +-- {: .standout} This is a sub-entry of * [[A Survey of Elliptic Cohomology]] an...
A Survey of Elliptic Cohomology - equivariant cohomology
https://ncatlab.org/nlab/source/A+Survey+of+Elliptic+Cohomology+-+equivariant+cohomology
<div class="rightHandSide toc"> [[!include cohomology - contents]] *** [[!include higher algebra - contents]] </div> +-- {: .standout} This is a sub-entry of * [[A Survey of Elliptic Cohomology]]. See there for background and context. This entry considers [[equivariant cohomology]] from the perspective of a...
A Survey of Elliptic Cohomology - formal groups and cohomology
https://ncatlab.org/nlab/source/A+Survey+of+Elliptic+Cohomology+-+formal+groups+and+cohomology
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Cohomology +--{: .hide} [[!include cohomology - contents]] =-- #### Higher geometry +--{: .hide} [[!include higher geometry - contents]] =-- #### Higher algebra +--{: .hide} [[!include higher algebra - contents]] =-- =-- =-...
A Survey of Elliptic Cohomology - the derived moduli stack of derived elliptic curves
https://ncatlab.org/nlab/source/A+Survey+of+Elliptic+Cohomology+-+the+derived+moduli+stack+of+derived+elliptic+curves
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Cohomology +--{: .hide} [[!include cohomology - contents]] =-- #### Higher geometry +--{: .hide} [[!include higher geometry - contents]] =-- #### Higher algebra +--{: .hide} [[!include higher algebra - contents]] =-- =-- =-- >**Abstract**...
A Survey of Elliptic Cohomology - towards a proof
https://ncatlab.org/nlab/source/A+Survey+of+Elliptic+Cohomology+-+towards+a+proof
<div class="rightHandSide toc"> [[!include higher algebra - contents]] </div> >**Abstract** This entry attempts to give an outline of a proof of Lurie's main theorem. +-- {: .standout} This is a sub-entry of * [[A Survey of Elliptic Cohomology]] see there for background and context. =-- Here are the entrie...
A-brane
https://ncatlab.org/nlab/source/A-brane
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### String theory +-- {: .hide} [[!include string theory - contents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Idea The [[branes]] of the [[A-model]] [[topological string]], hence a [[TQFT]]-shadow of the [[...
A-hat genus
https://ncatlab.org/nlab/source/A-hat+genus
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Index theory +-- {: .hide} [[!include index theory - contents]] =-- #### Cohomology +--{: .hide} [[!include cohomology - contents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Idea ### In terms of an ope...
A-infinity algebra > history
https://ncatlab.org/nlab/source/A-infinity+algebra+%3E+history
&lt; [[A-infinity algebra]] [[!redirects A-infinity algebra -- history]]
A-infinity category > history
https://ncatlab.org/nlab/source/A-infinity+category+%3E+history
&lt; [[A-infinity category]] [[!redirects A-infinity category -- history]]
A-infinity operad
https://ncatlab.org/nlab/source/A-infinity+operad
# The $A_\infty$ operad * table of contents {: toc} ##Idea An __$A_\infty$ operad__ is an [[operad]] over some [[enriched category theory|enriching category]] $C$ which is a (free) [[homological resolution|resolution]] of the standard [[associative operad]] enriched over $C$ (that is, the operad whose algebra...
A-infinity operad > history
https://ncatlab.org/nlab/source/A-infinity+operad+%3E+history
&lt; [[A-infinity operad]] [[!redirects A-infinity operad -- history]]
A-infinity-algebra
https://ncatlab.org/nlab/source/A-infinity-algebra
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Higher algebra +--{: .hide} [[!include higher algebra - contents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Idea An _$A_\infty$-algebra_ is a [[monoid]] internal to a [[homotopical category]] such that the ...
A-infinity-category
https://ncatlab.org/nlab/source/A-infinity-category
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Homological algebra +--{: .hide} [[!include homological algebra - contents]] =-- #### Higher category theory +--{: .hide} [[!include higher category theory - contents]] =-- =-- =-- #Contents# * table of contents ...
A-infinity-cocategory
https://ncatlab.org/nlab/source/A-infinity-cocategory
The concept _$A_\infty$-cocategory_ is the result of combining [[A-infinity-category]] with [[cocategory]].
A-infinity-module
https://ncatlab.org/nlab/source/A-infinity-module
## Idea __$A_\infty$-module__ $M$ over an $A_\infty$-algebra $A$ is an object with an $\infty$-[[infinity-representation|representation]] of $A$, modelled in the same formalism as the $A_\infty$-algebras are (usually in $k$-linear context, most often in (∞,1)-categories of chain complexes). In particular, one consid...
A-infinity-ring
https://ncatlab.org/nlab/source/A-infinity-ring
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Higher algebra +--{: .hide} [[!include higher algebra - contents]] =-- #### Higher linear algebra +-- {: .hide} [[!include homotopy - contents]] =-- #### Stable homotopy theory +--{: .hide} [[!include stable homotopy theor...
A-infinity-space
https://ncatlab.org/nlab/source/A-infinity-space
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Higher algebra +--{: .hide} [[!include higher algebra - contents]] =-- #### Homotopy theory +--{: .hide} [[!include homotopy - contents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Definition An **$A_\inf...
A-model
https://ncatlab.org/nlab/source/A-model
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### $\infty$-Chern-Simons theory +--{: .hide} [[!include infinity-Chern-Simons theory - contents]] =-- #### Quantum field theory +--{: .hide} [[!include functorial quantum field theory - contents]] =-- #### String theory +-- {: .hi...
A-n space
https://ncatlab.org/nlab/source/A-n+space
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Higher algebra +--{: .hide} [[!include higher algebra - contents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Definition An **$A_n$-space** or **$A_n$-algebra in spaces** is a space (in the sense of an [[homo...
A-theory
https://ncatlab.org/nlab/source/A-theory
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Cohomology +--{: .hide} [[!include cohomology - contents]] =-- #### Algebraic topology +--{: .hide} [[!include algebraic topology - contents]] =-- #### Representation theory +-- {: .hide} [[!include representation theory - con...
A. Ch. Ganchev
https://ncatlab.org/nlab/source/A.+Ch.+Ganchev
* [arXiv page](https://arxiv.org/search/hep-th?searchtype=author&query=Ganchev%2C+A) ## Selected writings On [[WZW models]] at [[rational number|fractional]] [[level (Chern-Simons theory)|level]]: * P. Furlan, [[A. Ch. Ganchev]], R. Paunov, [[Valentina B. Petkova]], *Solutions of the Knizhnik-Zamolodchikov E...
A. G. Walker
https://ncatlab.org/nlab/source/A.+G.+Walker
Arthur Geoffrey Walker was a professor at the University of Liverpool, working in [[differential geometry]], [[general relativity]], and [[cosmology]]. In particular, he is responsible for the [[Friedmann–Lemaître–Robertson–Walker metric]] in [[cosmology]]. ## Selected writings On [[vector fields as derivatio...
A. J. Tolland > history
https://ncatlab.org/nlab/source/A.+J.+Tolland+%3E+history
&lt; [[A. J. Tolland]]
A. P. Balachandran
https://ncatlab.org/nlab/source/A.+P.+Balachandran
__A. P. Balachandran__ is an indian-american theoretical physicist, retired from the Syracuse University. * [Wikipedia entry](https://en.wikipedia.org/wiki/A._P._Balachandran) ## Selected writings On the notion of [[entropy]] in [[quantum probability theory]]: * [[A. P. Balachandran]], T. R. Govindarajan, ...
A. Yung
https://ncatlab.org/nlab/source/A.+Yung
## Selected writings On [[vortex strings]] in $\mathcal{N}=2$ super QCD identified as [[superstrings]] in [[type II string theory]] [[KK-compactification|compactified]] on a [[conifold]]: * [[Mikhail Shifman]], [[A. Yung]], *Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories*...
A.A. Sharapov
https://ncatlab.org/nlab/source/A.A.+Sharapov
* [publications](http://arxiv.org/find/hep-th/1/au:+Sharapov_A/0/1/0/all/0/1) ## Selected writings On [[non-Lagrangian field theory]] such as [[self-dual higher gauge theory]]: * S. L. Lyakhovich, [[A. A. Sharapov]], _Quantizing non-Lagrangian gauge theories: an augmentation method_, JHEP 0701 047 (2007) &lb...
A1
https://ncatlab.org/nlab/source/A1
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ### Context #### Mathematics +-- {: .hide} [[!include mathematicscontents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Idea In the [[ADE-classification]], the items labeled $A1$ include the following: 1. as [[finite subgroup...
A1-cohesive homotopy type theory
https://ncatlab.org/nlab/source/A1-cohesive+homotopy+type+theory
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Type theory +-- {: .hide} [[!include type theory - contents]] =-- #### Topology +--{: .hide} [[!include topology - contents]] =-- #### Homotopy theory +--{: .hide} [[!include homotopy - contents]] =-- #### Algebra +--{: .hi...
a1-meson
https://ncatlab.org/nlab/source/a1-meson
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ### Context #### Fields and quanta +-- {: .hide} [[!include fields and quanta - table]] =-- =-- =-- #Contents# * table of contents {:toc} ## Idea The $a_1$-meson is the [[light meson]] which (in the [[Wigner classification]]) is the [[Lo...
A2
https://ncatlab.org/nlab/source/A2
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ### Context #### Mathematics +-- {: .hide} [[!include mathematicscontents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Idea In the [[ADE-classification]], the items labeled $A2$ include the following: 1. as [[finite subgro...
A3
https://ncatlab.org/nlab/source/A3
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ### Context #### Mathematics +-- {: .hide} [[!include mathematicscontents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Idea In the [[ADE-classification]], the items labeled $A3$ include the following: 1. as [[finite subgro...
A4-spatial groupoid > history
https://ncatlab.org/nlab/source/A4-spatial+groupoid+%3E+history
[[!redirects A4-spatial groupoid]] see discussion [here](https://nforum.ncatlab.org/discussion/14220/ktuply-associative-ngroupoid/?Focus=100308#Comment_100308)
Aarne Ranta
https://ncatlab.org/nlab/source/Aarne+Ranta
[webpage](http://www.cse.chalmers.se/~aarne/) ## Selected writings On [[dependent type theory]] and natural language (parsing and [[syntactic sugar|sugaring]]): * {#Ranta93} [[Aarne Ranta]], _Type theory and the informal language of mathematics_, TYPES '93: Proceedings of the international workshop on Types fo...
Aaron Bergman
https://ncatlab.org/nlab/source/Aaron+Bergman
* [arXiv entry](http://arxiv.org/find/hep-th/1/au:+Bergman_A/0/1/0/all/0/1) ## Selected writings On [[Bridgeland stability conditions]] for [[B-branes]] of the [[B-model]] [[topological string]]: * [[Aaron Bergman]], _Stability Conditions and Branes at Singularities_, Journal of High Energy Physics 2008.1...
Aaron F
https://ncatlab.org/nlab/source/Aaron+F
### September 2012 ### Wow, time flies! I'm now a Ph.D. student at UT Austin, and you can find some of my writing and stuff on my [department home page](http://www.ma.utexas.edu/users/afenyes). Things I'm thinking about these days include... * Quadratic differentials, [spectral networks](http://arxiv.org/abs/1204...
Aaron Greicius
https://ncatlab.org/nlab/source/Aaron+Greicius
* [webpage](http://greicius.wordpress.com/about-3/) category: people
Aaron Lauda
https://ncatlab.org/nlab/source/Aaron+Lauda
* [website](https://sites.google.com/view/lauda-home/home) ## Selected writings On [[Frobenius monads]] and [[ambidextrous adjunctions]] in [[2-categories]] more general than [[Cat]], with motivation from [[2d TQFT]]: * {#Lauda05} [[Aaron Lauda]], *Frobenius algebras and ambidextrous adjunctions*, Theory and...
Aaron M. Smith
https://ncatlab.org/nlab/source/Aaron+M.+Smith
* [GoogleScholar page](https://scholar.google.com/citations?user=e0yBkScAAAAJ) ## Selected writings On [[infinity-local systems|$\infty$-local systems]] in the sense of [[(infinity,1)-vector bundles|$(\infty,1)$-vector bundles]] with [[flat infinity-connections|flat $\infty$-connections]]: * [[Jonathan Block...
Aaron Mazel-Gee
https://ncatlab.org/nlab/source/Aaron+Mazel-Gee
* [webpage](http://etale.site/) ## Selected writing On [[tmf]]: * _You could've invented $tmf$_, April 2013 ([pdf slides](http://math.berkeley.edu/~aaron/writing/ustars-tmf-beamer.pdf)) Introducing [[model (infinity,1)-category|model $\infty$-category]]-theory: * [[Aaron Mazel-Gee]], *Model ∞-categories ...
Aaron Stump
https://ncatlab.org/nlab/source/Aaron+Stump
* [personal page](https://homepage.divms.uiowa.edu/~astump/) ## Selected writings On [[Agda]] as a [[certified programming|verified]] [[functional programming language]]: * [[Aaron Stump]], *Verified Functional Programming in Agda*, Association for Computing Machinery and Morgan & Claypool (2016) &lbrack;[do...
Ab
https://ncatlab.org/nlab/source/Ab
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ### Context #### Group Theory +-- {: .hide} [[!include group theory - contents]] =-- #### Category theory +-- {: .hide} [[!include category theory - contents]] =-- =-- =-- # Contents * table of contents {: toc} ## Idea _$Ab$_ denotes t...
Ab-enriched category
https://ncatlab.org/nlab/source/Ab-enriched+category
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Enriched category theory +--{: .hide} [[!include enriched category theory contents]] =-- #### Additive and abelian categories +--{: .hide} [[!include additive and abelian categories - contents]] =-- =-- =-- # $Ab$-enrich...
abc conjecture
https://ncatlab.org/nlab/source/abc+conjecture
#Contents# * table of contents {:toc} ## Idea The _abc conjecture_ (or _ABC conjecture_) is a [[number theory|number theoretic]] conjecture due to ([Oesterl&#233;-Masser 1985](#Oesterl&#233;Masser)), which says that there are only [[finite set|finitely many]] integer solutions to the [[equation]] $$ ...
Abdelmalek Abdesselam
https://ncatlab.org/nlab/source/Abdelmalek+Abdesselam
* [webpage](http://people.virginia.edu/~aa4cr/) ## related $n$Lab entries * [[renormalization group]] category: people
abductive reasoning
https://ncatlab.org/nlab/source/abductive+reasoning
#Contents# * table of contents {:toc} ##General idea **Abductive** [[reasoning]] is a process whereby one reasons to the truth of an explanation from its ability to account for what is observed. It is therefore sometimes also known as **inference to the best explanation**. [[Charles Peirce]], the originator ...
Abdus Salam
https://ncatlab.org/nlab/source/Abdus+Salam
* [Wikipedia entry](http://en.wikipedia.org/wiki/Abdus_Salam) ## Selected writings Co-introducing the theory of the [[electroweak field]]: * [[Abdus Salam]], [[John Clive Ward]], *Weak and electromagnetic interactions*, Nuovo Cimento. **11** 4 (1959) 568–577 &lbrack;[doi:10.1007/BF02726525](https://doi.org/1...
Abel-Jacobi map
https://ncatlab.org/nlab/source/Abel-Jacobi+map
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ### Context #### Complex geometry +--{: .hide} [[!include complex geometry - contents]] =-- #### Differential cohomology +--{: .hide} [[!include differential cohomology - contents]] =-- =-- =-- #Contents# * table of contents {:toc} ## I...
abelian 2-category
https://ncatlab.org/nlab/source/abelian+2-category
[[abelian category|Abelian categories]] are a common generalization of the category of abelian groups, categories of $R$-modules where $R$ is a ring, and the categories of sheaves of $\mathcal{O}_X$-modules where $\mathcal{O}_X$ is a sheaf of rings on a topological space $X$. Similarly, in the categorical dimension 2, ...
abelian 3-group
https://ncatlab.org/nlab/source/abelian+3-group
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Group Theory +-- {: .hide} [[!include group theory - contents]] =-- #### $(\infty,1)$-Category theory +--{: .hide} [[!include quasi-category theory contents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Definition An _abelian 3...
abelian 4-group
https://ncatlab.org/nlab/source/abelian+4-group
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Group Theory +-- {: .hide} [[!include group theory - contents]] =-- #### $(\infty,1)$-Category theory +--{: .hide} [[!include quasi-category theory contents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Definition An _abelian ...
abelian 7-group
https://ncatlab.org/nlab/source/abelian+7-group
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Group Theory +-- {: .hide} [[!include group theory - contents]] =-- #### $(\infty,1)$-Category theory +--{: .hide} [[!include quasi-category theory contents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Definition An _abelian...
Abelian categories with applications to rings and modules
https://ncatlab.org/nlab/source/Abelian+categories+with+applications+to+rings+and+modules
This page compiles pointers related to: * [[Nicolae Popescu]]: \linebreak __Abelian categories with applications to rings and modules__ \linebreak London Mathematical Society Monographs **3* Academic Press (1973) [MR0340375](http://www.ams.org/mathscinet-getitem?mr=0340375) on th...
abelian category
https://ncatlab.org/nlab/source/abelian+category
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Enriched category theory +--{: .hide} [[!include enriched category theory contents]] =-- #### Additive and abelian categories +--{: .hide} [[!include additive and abelian categories - contents]] =-- #### Homological algebra +--...
abelian differential graded Lie algebra
https://ncatlab.org/nlab/source/abelian+differential+graded+Lie+algebra
An abelian [[differential graded Lie algebra]] is a [[cochain complex]] seen as a differential graded Lie algebra with trivial [[Lie algebra|Lie bracket]]. In the particular case when the cochain complex is concentrated in degree zero, one recovers the notion of [[abelian Lie algebra]].
abelian group
https://ncatlab.org/nlab/source/abelian+group
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Group Theory +-- {: .hide} [[!include group theory - contents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Definition An _abelian group_ (named after [[Niels Henrik Abel]]) is a [[group]] $A$ where the multip...
abelian infinity-group
https://ncatlab.org/nlab/source/abelian+infinity-group
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Group Theory +-- {: .hide} [[!include group theory - contents]] =-- #### Higher algebra +--{: .hide} [[!include higher algebra - contents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Idea An ordinary [[...
abelian Lie algebra
https://ncatlab.org/nlab/source/abelian+Lie+algebra
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### $\infty$-Lie theory +--{: .hide} [[!include infinity-Lie theory - contents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Definition A [[Lie algebra]] $\mathfrak{g}$ is __abelian__ if its bracket is identically 0, in that for al...
abelian model category
https://ncatlab.org/nlab/source/abelian+model+category
## Idea An abelian model category is an [[abelian category]] with a compatible [[model structure]]. ## Definition An **abelian model category** is an [[abelian category]] $\mathcal{A}$ that is [[complete category|complete]] and [[cocomplete category|cocomplete]], together with a [[model structure]] such that * (AMC...
abelian sheaf
https://ncatlab.org/nlab/source/abelian+sheaf
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Additive and abelian categories +--{: .hide} [[!include additive and abelian categories - contents]] =-- #### Topos Theory +-- {: .hide} [[!include topos theory - contents]] =-- =-- =-- > see also _[[sheaf of abelian gro...
abelian sheaf cohomology
https://ncatlab.org/nlab/source/abelian+sheaf+cohomology
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Cohomology +--{: .hide} [[!include cohomology - contents]] =-- #### $(\infty,1)$-Topos Theory +--{: .hide} [[!include (infinity,1)-topos - contents]] =-- =-- =-- #Contents# * table of contents {:toc} ##Idea## ### G...
abelian subcategory
https://ncatlab.org/nlab/source/abelian+subcategory
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ### Context #### Notions of subcategory +-- {: .hide} [[!include notions of subcategory]] =-- #### Homological algebra +--{: .hide} [[!include homological algebra - contents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Definition For $\mathcal{A...
abelian variety
https://ncatlab.org/nlab/source/abelian+variety
#Contents# * table of contents {:toc} ## Idea Abelian varieties are higher dimensional analogues of [[elliptic curve]]s (which are included) -- they are [[varieties]] equipped with a structure of an [[abelian group]], hence abelian [[group schemes]], whose multiplication and inverse are regular maps. ## De...
abelianization
https://ncatlab.org/nlab/source/abelianization
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ### Context #### Category theory +-- {: .hide} [[!include category theory - contents]] =-- #### Group Theory +-- {: .hide} [[!include group theory - contents]] =-- =-- =-- # Contents * table of contents {: toc} ## Idea Abelianisation i...
Abhijit Champanerkar
https://ncatlab.org/nlab/source/Abhijit+Champanerkar
* [webpage](https://www.math.csi.cuny.edu/abhijit/) ## Selected writings On [[knot theory]], [[knot complements]], etc.: * [[Abhijit Champanerkar]], _The geometry of knot complements_ ([pdf](https://www.math.csi.cuny.edu/~abhijit/talks/knot-geometry-h.pdf), [[ChampanerkarKnotComplements.pdf:file]]) cate...
Abhijit Gadde
https://ncatlab.org/nlab/source/Abhijit+Gadde
* [Institute page](http://qst.theory.tifr.res.in/StringTheoryStud/faculty1.php) * [InSpire page](https://inspirehep.net/authors/1065230) ## Selected writings On [[KK-compactification]] of [[D=6 N=(2,0) SCFT]] on [[4-manifolds]] to [[2d CFTs]]: * [[Abhijit Gadde]], [[Sergei Gukov]], [[Pavel Putrov]], *Fi...
Abhishek Banerjee
https://ncatlab.org/nlab/source/Abhishek+Banerjee
* [personal page](https://sites.google.com/site/abhishekb1313/) * [MathGenealogy page](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=132991) ## Selected writings Discussion of [[opposite categories]] of [[commutative monoids in a symmetric monoidal category]] regarded as categories of generalized [[aff...
ABJM theory
https://ncatlab.org/nlab/source/ABJM+theory
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ### Context #### $\infty$-Chern-Simons theory +--{: .hide} [[!include infinity-Chern-Simons theory - contents]] =-- #### String theory +-- {: .hide} [[!include string theory - contents]] =-- =-- =-- #Contents# * table of contents {:toc} ...
AbMon > history
https://ncatlab.org/nlab/source/AbMon+%3E+history
[[!redirects AbMon]] The [[category]] of commutative (abelian) [[monoids]]. category: category [[!redirects Ab Mon]]
Abner Shimony
https://ncatlab.org/nlab/source/Abner+Shimony
* [Wikipedia entry](https://en.wikipedia.org/wiki/Abner_Shimony) * Alisa Bokulich and Don Howard: *[Abner Shimony (1928-2015)](https://www.bu.edu/cphs/about/abner-shimony/)* ## Selected writings On [[Bell's theorem]] in [[quantum physics]]: * [[John F. Clauser]], [[Abner Shimony]], *Bell's theorem. Expe...
About
https://ncatlab.org/nlab/source/About
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Contents### {: .clickToReveal} ###Contents### {: .clickToHide tabindex="0"} +--{: .hide} [[!include contents]] =-- =-- =-- #Contents# * table of contents {:toc} ## History {#History} The [[HomePage|nLab]] is a _collaborative [wiki](ht...
Abraham Adrian Albert
https://ncatlab.org/nlab/source/Abraham+Adrian+Albert
* [Wikipedia entry](https://en.wikipedia.org/wiki/Abraham_Adrian_Albert) ## related $n$Lab entries * [[Albert algebra]] category:people [[!redirects Abraham Albert]] [[!redirects Adrian Albert]]
Abraham Fraenkel
https://ncatlab.org/nlab/source/Abraham+Fraenkel
Abraham Fraenkel was a mathematician who worked on [[set theory]] and [[foundations]]. He is responsible for the 'F' in [[ZFC]], but also did work using [[ZFA]]. Among other things, he also introduced the [[basic Fraenkel model|basic]] and [[second Fraenkel model|second Fraenkel models]], early examples of [[forcing]]...
Abraham Robinson
https://ncatlab.org/nlab/source/Abraham+Robinson
Abraham Robinson was a German born mathematician, who studied in Jerusalem, before taking up various positions in France then in Cranfield (the staff college of the RAF in the UK, during the second world war), Israel, Canada and finally in the USA at UCLA and Yale. He is the 'father' of Nonstandard Analysis, the first ...
Abraham Westerbaan
https://ncatlab.org/nlab/source/Abraham+Westerbaan
* [personal page](https://bram.westerbaan.name/home/about.html) * [GoogleScholar page](https://scholar.google.com/citations?user=6Hz9H7sAAAAJ&hl=en) ## Selected writings On [[categorical semantics]] of [[quantum programming languages]] on [[von Neumann algebras]] for the [[quantum lambda-calculus]]: * [[K...
abrupt category
https://ncatlab.org/nlab/source/abrupt+category
Each [[category with star-morphisms]] gives rise to a category (<b>abrupt category</b>, see a remark below why I call it "abrupt"), as described below. Below for simplicity I assume that the set $M$ and the set of our indexed families of functions are disjoint. The general case (when they are not necessarily disjoint) ...
absolute coequalizer
https://ncatlab.org/nlab/source/absolute+coequalizer
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ### Context #### Category theory +-- {: .hide} [[!include category theory - contents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Definition An **absolute coequalizer** in a [[category]] $C$ is a [[coequalizer]] which is preserve...
absolute cohomology
https://ncatlab.org/nlab/source/absolute+cohomology
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Cohomology +--{: .hide} [[!include cohomology - contents]] =-- #### Geometry +--{: .hide} [[!include higher geometry - contents]] =-- =-- =-- ## Contents * table of contents {:toc} ## Idea Roughly something like a combination of a "[[geo...
absolute colimit
https://ncatlab.org/nlab/source/absolute+colimit
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Limits and colimits +--{: .hide} [[!include infinity-limits - contents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Idea An **absolute colimit** is a [[colimit]] which is [[preserved limit|preserved]] by any [[...
absolute conclusion
https://ncatlab.org/nlab/source/absolute+conclusion
[[!redirects agar.io]] +-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ### Context #### Philosophy +-- {: .hide} [[!include philosophy - contents]] =-- #### Foundations +-- {: .hide} [[!include foundations - contents]] =-- =-- =-- # Contents * table of contents {:toc} [[!redirects Abs...
absolute convergence
https://ncatlab.org/nlab/source/absolute+convergence
+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ### Context #### Analysis +-- {: .hide} [[!include analysis - contents]] =-- =-- =-- \tableofcontents ## Definition ### For series in the real numbers In [[real analysis]], given a sequence $a:\mathbb{N} \to \mathbb{R}$ in the [[real numb...