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Part of higher category theory that for instance in Algebraic Topology enables us to capture finer homotopic distinctions. As in say Eilenberg-Maclane spaces.

13 votes
2 answers
3k views

Can we use Mann's six-functor formalism with D-modules?

In a recent course in Bonn, P. Scholze explains a formalization of a six-functor formalism due to L. Mann. In this axiomatization, three of the functors $f_!,f^*,\otimes$ are "constructed" (in the for …
Gabriel's user avatar
  • 721
7 votes
1 answer
406 views

Intuition for isofibrations in $\infty$-categories

In the very first chapter of Elements of $\infty$-category theory, E. Riehl and D. Verity define their notion of an $\infty$-cosmos, which should axiomatise a category in which $\infty$-categories liv …
Gabriel's user avatar
  • 721
29 votes
1 answer
4k views

Why stable $\infty$-categories?

I begin by saying that while I understand what a triangulated / derived category is pretty well, I know nothing about Higher Algebra stuff and not even $\infty$-categories. I've heard some people say …
Gabriel's user avatar
  • 721