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David Michael Roberts (Nov 15 2020 at 09:24):Since I was shamelessly self-promoting on Twitter, I can't lower myself further by repeating it here:
https://twitter.com/HigherGeometer/status/1327792723693170688
As a student I proved a version of Quillen's Theorem A for categories internal to Top. The statement was lurking on my private nLab pages, though not the proof. Anyone interested to see it?
- theHigherGeometer (@HigherGeometer)https://twitter.com/HigherGeometer/status/1327825343000940544
Part of the point was to get a homotopy equivalence, not just a weak equivalence. https://ncatlab.org/davidroberts/show/Theorem+A+for+topological+categories The proof only uses technology available to Quillen at the time of the original Theorem A. I should polish and release the pdf, last edited in 2008, in case it's useful.
- theHigherGeometer (@HigherGeometer) David Michael Roberts (Nov 15 2020 at 09:28):I'm sure this could be proved with some very high-powered stuff, but I have a soft spot for basic/elementary proofs of things that shouldn't be hard.
David Michael Roberts (Nov 15 2020 at 11:11):Gah, might be wrong stream. Should be in alg top, maybe?
Notification Bot (Nov 15 2020 at 11:45):This topic was moved here from #theory: category theory > Theorem A for topological categories by Matteo Capucci
David Michael Roberts (Nov 15 2020 at 13:42):Thanks @Matteo Capucci :-)
Matteo Capucci (he/him) (Nov 15 2020 at 13:59)::blush: