Timeline for Reference request: the free adjunction being free as an $(\infty, 2)$-category?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 28, 2023 at 15:19 | vote | accept | nrkm | ||
| Sep 28, 2023 at 14:27 | comment | added | nrkm | Ah, ok. I think that follows from the rectification of enriched $\infty$-categories (Theorem 5.8 of arxiv.org/pdf/1312.3881.pdf for V=Joyal model structure on sSet.). | |
| Sep 28, 2023 at 14:00 | comment | added | nrkm | Thank you (the point you mentioned was a part of my confusion)! I think I'll accept this answer, but here's another part of the confusion: R-V paper states the theorem in terms of simplicial categories, and I was not sure if that takes care of all $(\infty, 2)$-categories. I guess it follows from generality that there is a model structure on simplicial categories where fibrant objects are quasi-category-enriched categories and cofibrations are simplicial subcomputad inclusions. Is it shown to be equivalent to $\mathrm{Cat}_{(\infty, 2)}$? | |
| Sep 28, 2023 at 8:00 | comment | added | Peter LeFanu Lumsdaine | Worth adding that although the free $(\infty,2)$-category OP describes (call it $\newcommand{\Adj}{\mathrm{Adj}}\newcommand{\Adjwk}{\Adj_\mathrm{wk}}\Adjwk$) isn’t quite equivalent to $\Adj$ it’s true nonetheless that providing those generators suffices to present a map out of $\Adj$ — it’s just slightly overdetermined, as you say, so it’s not an equivalence but a retraction from $\Adjwk$ onto $\Adj$. | |
| Sep 28, 2023 at 7:52 | history | answered | Maxime Ramzi | CC BY-SA 4.0 |