Timeline for Are locally fully faithful 2-functors closed under 2-pushout in 2-Cat?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Feb 20, 2022 at 2:59 | vote | accept | varkor | ||
| Feb 20, 2022 at 1:57 | history | edited | Tim Campion | CC BY-SA 4.0 |
added 286 characters in body
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| Feb 19, 2022 at 20:04 | comment | added | Tim Campion | If I were trying to prove your conjecture to be true, this should not suffice. But I’m proving it false, ie coming up with a counterexample. so it does suffice. | |
| Feb 19, 2022 at 20:03 | comment | added | varkor | Thank you, this is the observation I had overlooked. Could you add the elaboration in these comments to your answer? Then I'll accept it :) | |
| Feb 19, 2022 at 20:00 | comment | added | Tim Campion | Let F: A —> B be a functor between 1-categories. Let i(F): i(A) —> i(B) be the corresponding 2-functor between locally discrete 2-categories. Then F is faithful iff i(F) is locally fully faithful. | |
| Feb 19, 2022 at 19:50 | comment | added | varkor | It's still not clear to me why it suffices to consider only the faithful functors. I'm interested in locally fully faithful functors: why is it still sufficient if we drop fullness? | |
| Feb 17, 2022 at 4:12 | comment | added | Tim Campion | I'm including 1-categories into 2-categories as the locally discrete ones. This functor has a right adjoint, so it preserves pushouts. | |
| Feb 17, 2022 at 3:32 | comment | added | varkor | I'm probably missing something obvious, but why does it suffice to show that faithful functors are not closed under pushout? Why faithful and not fully faithful (which are closed under pushout)? | |
| Feb 17, 2022 at 2:48 | history | answered | Tim Campion | CC BY-SA 4.0 |