title stringlengths 1 131 | url stringlengths 33 167 | content stringlengths 0 637k |
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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 |
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### Context
#### Philosophy
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[[!include philosophy - contents]]
=--
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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}
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###Context###
#### Mapping space
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[[!include mapping space - contents]]
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## 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 |
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###Context###
#### Monoidal categories
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[[!include monoidal categories - contents]]
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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 |
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#### Cohomology
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[[!include cohomology - contents]]
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#### Higher geometry
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[[!include higher geometry - contents]]
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#### Higher algebra
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[[!include higher algebra - contents]]
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... |
A Survey of Elliptic Cohomology - A-equivariant cohomology | https://ncatlab.org/nlab/source/A+Survey+of+Elliptic+Cohomology+-+A-equivariant+cohomology |
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#### Cohomology
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[[!include cohomology - contents]]
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#### Higher algebra
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[[!include higher algebra - contents]]
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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 |
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###Context###
#### Cohomology
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[[!include cohomology - contents]]
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#### Higher geometry
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[[!include higher geometry - contents]]
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#### Higher algebra
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[[!include higher algebra - contents]]
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... |
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 $M_{1,1}$.
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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]]
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#### Higher algebra
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[[!include higher algebra - contents]]
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>**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 |
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#### Cohomology
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[[!include cohomology - contents]]
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#### Higher geometry
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[[!include higher geometry - contents]]
=--
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+-- {: .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 |
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#### Cohomology
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[[!include cohomology - contents]]
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[[!include higher geometry - contents]]
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#### Higher algebra
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[[!include higher algebra - contents]]
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=-... |
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 |
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#### Cohomology
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[[!include cohomology - contents]]
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#### Higher geometry
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[[!include higher geometry - contents]]
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#### Higher algebra
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[[!include higher algebra - contents]]
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>**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 |
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#### String theory
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[[!include string theory - contents]]
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#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 |
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#### Index theory
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#### Cohomology
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[[!include cohomology - contents]]
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#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 | < [[A-infinity algebra]]
[[!redirects A-infinity algebra -- history]] |
A-infinity category > history | https://ncatlab.org/nlab/source/A-infinity+category+%3E+history | < [[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 | < [[A-infinity operad]]
[[!redirects A-infinity operad -- history]] |
A-infinity-algebra | https://ncatlab.org/nlab/source/A-infinity-algebra |
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#### Higher algebra
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[[!include higher algebra - contents]]
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#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 |
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#### Homological algebra
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[[!include homological algebra - contents]]
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#### Higher category theory
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[[!include higher category theory - contents]]
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#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 |
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#### Higher algebra
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[[!include higher algebra - contents]]
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#### Higher linear algebra
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[[!include homotopy - contents]]
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#### Stable homotopy theory
+--{: .hide}
[[!include stable homotopy theor... |
A-infinity-space | https://ncatlab.org/nlab/source/A-infinity-space |
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#### Higher algebra
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#### Homotopy theory
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[[!include homotopy - contents]]
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#Contents#
* table of contents
{:toc}
## Definition
An **$A_\inf... |
A-model | https://ncatlab.org/nlab/source/A-model |
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#### $\infty$-Chern-Simons theory
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#### Quantum field theory
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[[!include functorial quantum field theory - contents]]
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#### String theory
+-- {: .hi... |
A-n space | https://ncatlab.org/nlab/source/A-n+space |
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#### Higher algebra
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[[!include higher algebra - contents]]
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#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 |
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#### Cohomology
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[[!include cohomology - contents]]
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#### Algebraic topology
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[[!include algebraic topology - contents]]
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#### Representation theory
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[[!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 | < [[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 |
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### Context
#### Mathematics
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[[!include mathematicscontents]]
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=--
=--
#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 |
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#### Type theory
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[[!include type theory - contents]]
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#### Topology
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[[!include topology - contents]]
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#### Homotopy theory
+--{: .hide}
[[!include homotopy - contents]]
=--
#### Algebra
+--{: .hi... |
a1-meson | https://ncatlab.org/nlab/source/a1-meson |
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### 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 |
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### Context
#### Mathematics
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[[!include mathematicscontents]]
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#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 |
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### 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) [[do... |
Ab | https://ncatlab.org/nlab/source/Ab |
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### Context
#### Group Theory
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[[!include group theory - contents]]
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#### Category theory
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[[!include category theory - contents]]
=--
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# Contents
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## Idea
_$Ab$_ denotes t... |
Ab-enriched category | https://ncatlab.org/nlab/source/Ab-enriched+category |
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abc conjecture | https://ncatlab.org/nlab/source/abc+conjecture |
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## Idea
The _abc conjecture_ (or _ABC conjecture_) is a [[number theory|number theoretic]] conjecture due to ([Oesterlé-Masser 1985](#OesterléMasser)), 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 [[doi:10.1007/BF02726525](https://doi.org/1... |
Abel-Jacobi map | https://ncatlab.org/nlab/source/Abel-Jacobi+map |
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## 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 |
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## Definition
An _abelian 3... |
abelian 4-group | https://ncatlab.org/nlab/source/abelian+4-group |
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## Definition
An _abelian ... |
abelian 7-group | https://ncatlab.org/nlab/source/abelian+7-group |
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## 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 |
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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 |
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## 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 |
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## Idea
An ordinary [[... |
abelian Lie algebra | https://ncatlab.org/nlab/source/abelian+Lie+algebra |
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## 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 |
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> see also _[[sheaf of abelian gro... |
abelian sheaf cohomology | https://ncatlab.org/nlab/source/abelian+sheaf+cohomology |
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##Idea##
### G... |
abelian subcategory | https://ncatlab.org/nlab/source/abelian+subcategory |
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## 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 |
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* 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 |
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... |
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 |
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## 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 |
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## Definition
An **absolute coequalizer** in a [[category]] $C$ is a [[coequalizer]] which is preserve... |
absolute cohomology | https://ncatlab.org/nlab/source/absolute+cohomology |
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## Contents
* table of contents
{:toc}
## Idea
Roughly something like a combination of a "[[geo... |
absolute colimit | https://ncatlab.org/nlab/source/absolute+colimit |
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* table of contents
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## 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]]
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# Contents
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{:toc}
[[!redirects Abs... |
absolute convergence | https://ncatlab.org/nlab/source/absolute+convergence |
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\tableofcontents
## Definition
### For series in the real numbers
In [[real analysis]], given a sequence $a:\mathbb{N} \to \mathbb{R}$ in the [[real numb... |
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