Timeline for Monomorphisms of diagrams in an $\infty$-category
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 26, 2023 at 19:54 | comment | added | Mike Shulman | If $C$ is not finitely complete, then it is still true that a pointwise monomorphism is a monomorphism in the functor category, but in that case the converse can fail. There is a counterexample in section 3.3 of Kelly's Basic concepts of enriched category theory. | |
| Jun 26, 2023 at 19:23 | comment | added | Maxime Ramzi | (note that the first part does not need $C$ to be finitely complete: you can always embed the question in the category of presheaves) For the general case, I said it elsewhere but I might as well write it here : I believe (but can't prove yet) that it should hold if $K$ is weakly contractible. As Daniel points out, products or things like $BG$ yield counterexamples | |
| Jun 26, 2023 at 19:12 | comment | added | Jonathan Beardsley | Wow thanks, that's wonderful! And yeah, I suppose part 2 could maybe depend on something like connectedness of the diagram, or filteredness, or some kind of thing like that. | |
| Jun 26, 2023 at 19:08 | history | answered | daniel gratzer | CC BY-SA 4.0 |