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Results tagged with ct.category-theory
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user 51424
Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
7
votes
1
answer
292
views
Proposition in HTT on cofibrations of categories
Proposition A.3.3.9. in Higher Topos Theory is as follows:
Let $S$ be an excellent model category and let $f:C\rightarrow C'$ be a cofibration of small $S$-enriched categories. Then (1) for every …
- 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