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Results tagged with higher-category-theory
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user 51424
For questions involving one or more categorical dimensions, or involving homotopy coherent categorical structures.
8
votes
Accepted
Remark 2.4.1.4 Higher Topos Theory
Let's see what the data of a diagram
\begin{matrix}
\partial\Delta^{n-2}&{\to}&X_{/f}\\
\downarrow &&\downarrow\\
\Delta^{n-2}&{\to}&X_{/y}\times_{S_{/p(y)}}S_{p(f)}\end{matrix}
translates to. I cl …
- 5,958
5
votes
0
answers
312
views
Tensor product of t-structures compatible with filtered colimits
Let $C,D$ be two stable presentable $(\infty,1)$-categories, equipped with accessible t-structures. Then you can define an accessible t-structure on $C\otimes D$ by having $(C\otimes D)_{\geq 0}$ be g …
- 5,958
10
votes
Why do we care about $(\infty,2)$-categories?
One place where $(\infty,2)$-categories shows up is the geometric Langlands program. (As in David Ben-Zvi's comment, this is again related to the TFT example.) Indeed, local geometric Langlands is oft …
- 5,958
39
votes
2
answers
2k
views
What parts of the theory of quasicategories have been simplified since the publication of HTT?
It has been almost ten years since Lurie published Higher Topos Theory, where (following Joyal and probably others) he set up foundations for higher category theory via quasicategories. My impression …
- 5,958