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Results tagged with ct.category-theory
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user 102390
Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
5
votes
Is there a Hopf algebra-style description of chain complexes?
$\newcommand{\AA}{\mathbf{A}}\newcommand{\GG}{\mathbf{G}}\newcommand{\Mod}{\mathrm{Mod}}\newcommand{\fil}{\mathrm{fil}}\newcommand{\QCoh}{\mathrm{QCoh}} \newcommand{\spec}{\mathrm{Spec}}$Let $R$ be a …
- 5,520
1
vote
Can tangent ($\infty$,1)-categories be described in terms of the higher Grothendieck constru...
See the proof of Proposition 1.1.9 here https://arxiv.org/pdf/0709.3091v2.pdf.
- 5,520
1
vote
Relation between different definitions of homotopy
$\newcommand{\Z}{\mathbf{Z}}$I'll talk about chain complexes over $\Z$ (although this works for any ring $R$). It looks like you're talking about cochain complexes in the question. Let $I$ be the anal …
- 5,520
15
votes
Natural examples of $(\infty,n)$-categories for large $n$
$\newcommand{\Vect}{\mathrm{Vect}} \newcommand{\Mod}{\mathrm{Mod}} \newcommand{\cc}{\mathbf{C}}$Here are three (related) examples. The first one is simple (although not really related to physics): an …
9
votes
Which $\infty$-groupoids correspond to simplicial abelian groups?
$\newcommand{\Z}{\mathbf{Z}} \newcommand{\Mod}{\mathrm{Mod}}$Note that if $\Mod^{\geq 0}_\Z$ denotes the category of connective $\mathrm{H}\Z$-module spectra, then by the Dold-Kan correspondence and t …
- 5,520
17
votes
Accepted
Unifying "cohomology groups classify extensions" theorems
$\newcommand{\cA}{\mathcal{A}}\newcommand{\Ext}{\mathrm{Ext}}\newcommand{\Hom}{\mathrm{Hom}}$Let $\cA$ be an abelian category; then, $\Ext_\cA^i(A,B)$ is literally $\Hom_{D(\cA)}(A, B[i])$, where $B[i …
- 5,520
5
votes
Any news about equivalences of periodic triangulated or $\infty$-categories?
$\newcommand{\QCoh}{\mathrm{QCoh}} \newcommand{\Mod}{\mathrm{Mod}} \newcommand{\LMod}{\mathrm{LMod}} \newcommand{\spec}{\mathrm{Spec}} \newcommand{\Fun}{\mathrm{Fun}} \newcommand{\Z}{\mathbf{Z}} \newc …
- 5,520
7
votes
Definition of $E_n$-modules for an $E_n$-algebra
$\newcommand{\E}{\mathbf{E}} \newcommand{\Mod}{\mathrm{Mod}} \newcommand{\cc}{\mathcal{C}}$Here's one way to think about $\E_n$-modules. Let $R$ be an $\E_n$-ring (in a presentable symmetric monoidal …
- 5,520
10
votes
Surveys of Goodwillie Calculus
This is 7 years too late, but this survey (to appear in the Handbook of Homotopy Theory) is a really readable survey of Goodwillie calculus: https://arxiv.org/abs/1902.00803.
- 5,520