@highergeometer@mathstodon.xyz
Post #1684313
2026-04-22 07:06 UTC
@antoinechambertloir It's foundational category theory stuff, and you can see a sample of the difference between Makkai's definition at https://en.wikipedia.org/wiki/Anafunctor#Set-theoretic_definition and the definition in the previous definition (a span of functors where the backwards one is ff and surjective on objects - sadly the notation on that page is inconsistent, with |F| standing for both a class/set and a category).
Paper: https://doi.org/10.1016/0022-4049(95)00029-1
Replies (1)
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@highergeometer@mathstodon.xyz 2026-04-22 07:10
@antoinechambertloir I have my own approach: http://tac.mta.ca/tac/volumes/26/29/26-29abs.html But what I proved is more or less disjoint from what Makkai proved, which was aimed purely at straight-up category theory and usual tools for that. I was aiming at what I needed for dealing with geometric stacks.