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20 votes
2 answers
1k views

Commutative rings : Topoi = Fields :?

The following is probably a bad question, but hopefully, it might have a very good answer. In category theory there is a quite famous analogy between topoi and commutative rings, I was never ...
Ivan Di Liberti's user avatar
68 votes
4 answers
5k views

Why did Voevodsky consider categories "posets in the next dimension", and groupoids the correct generalisation of sets?

Earlier today, I stumbled upon this article written by V. Voevodsky about the "philosophy" behind the Univalent Foundations program. I had read it before around the time of his passing, and one ...
Soham Chowdhury's user avatar
25 votes
2 answers
1k views

Nice application of generalized smooth spaces

I am a fan of category theory in general, and I appreciate that various brands of generalized smooth spaces (Diffeological spaces, Chen spaces, Frolicher spaces ...) form much nicer categories of ...
5 votes
2 answers
624 views

Motivation for the covariant model structure on SSet/S

I was reading HTT 2.1.4, and I just totally lost what was going on. Could someone provide some motivation for this section? Why do we want another model structure? I'm sorry for not providing ...
Harry Gindi's user avatar
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