Martin Escardo on Nostr: Somebody asked, in mathoverflow, "What is the motivation for infinity category ...
Somebody asked, in mathoverflow, "What is the motivation for infinity category theory?" [1].
The end of the answer by D.-C. Cisinski is the following (but it is also worth reading the beginning):
"At the end of the day, ∞-category theory looks very much like ordinary category theory, except that we can always reduce our computations to contexts in which there is only one way to identify objects: isomorphisms. This has to be compared with the zoo: equality, isomorphism, equivalence of categories, equivalence of 2-categories, homotopy equivalence, quasi-isomorphisms... That turns the process of gluing mathematical objects much more natural (in fact possible) in ∞-category theory, which is the basic tool to do any kind of geometry. That is why there is no turning back, I think."
[1] https://mathoverflow.net/questions/450835/what-is-the-motivation-for-infinity-category-theory
1/
The end of the answer by D.-C. Cisinski is the following (but it is also worth reading the beginning):
"At the end of the day, ∞-category theory looks very much like ordinary category theory, except that we can always reduce our computations to contexts in which there is only one way to identify objects: isomorphisms. This has to be compared with the zoo: equality, isomorphism, equivalence of categories, equivalence of 2-categories, homotopy equivalence, quasi-isomorphisms... That turns the process of gluing mathematical objects much more natural (in fact possible) in ∞-category theory, which is the basic tool to do any kind of geometry. That is why there is no turning back, I think."
[1] https://mathoverflow.net/questions/450835/what-is-the-motivation-for-infinity-category-theory
1/