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Results tagged with higher-category-theory
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user 102390
For questions involving one or more categorical dimensions, or involving homotopy coherent categorical structures.
31
votes
Accepted
Spectral algebraic geometry vs derived algebraic geometry in positive characteristic?
I'll try to answer this question from the topological viewpoint. The short summary is that structured objects in the spectral setting have cohomology operations and power operations, which forces spec …
- 5,520
10
votes
Accepted
Homotopy coherent generalization of classifying space theory
$\newcommand{\cS}{\mathcal{S}}\newcommand{\Fun}{\mathrm{Fun}}\newcommand{\LMod}{\mathrm{LMod}}\newcommand{\Sp}{\mathrm{Sp}}$Hey Laurent :) Let $X$ be a space (which I'll view as a Kan complex), and le …
- 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
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 …
6
votes
Accepted
Spectral and derived deformations of schemes
In general, these are incredibly hard questions. It seems to me that one natural question to ask (if you are interested in $\pi_0$ of ring spectra) would be about understanding even periodic $\mathbf{ …
- 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