Timeline for Are locally fully faithful 2-functors closed under 2-pushout in 2-Cat?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 20, 2022 at 2:59 | vote | accept | varkor | ||
| Feb 17, 2022 at 2:48 | answer | added | Tim Campion | timeline score: 1 | |
| Dec 14, 2021 at 22:58 | comment | added | Tim Campion | Ok -- so that's the same thing as a $Cat$-enriched pushout. Because $Cat$ has cotensors, this is the same thing as a pushout in the underlying 1-category $Cat$. | |
| Dec 14, 2021 at 22:03 | comment | added | varkor | @TimCampion: I mean a strict 2-colimit over a span, i.e. the dual of the definition of strict 2-pullback on the nLab. | |
| Dec 14, 2021 at 18:16 | comment | added | Tim Campion | @varkor But I don't know what a 2-pushout is. Is it a cocomma object? Is it a lax pushout? Or is it simply a pushout? Oh... does it mean "Cat-enriched pushout"? | |
| Dec 14, 2021 at 18:16 | history | edited | varkor | CC BY-SA 4.0 |
added 11 characters in body
|
| Dec 14, 2021 at 18:15 | comment | added | varkor | @TimCampion: I mean strict 2-pushout. I'm using "pseudopushout" for the full weak version. I'll update the question to make that clearer, though. | |
| Dec 14, 2021 at 17:34 | comment | added | Tim Campion | What do you mean by "2-pushout"? Do you just mean "fully weak pushout"? | |
| Nov 6, 2021 at 3:39 | history | edited | varkor | CC BY-SA 4.0 |
added 71 characters in body
|
| Nov 6, 2021 at 3:13 | comment | added | David Roberts♦ | OK, thanks! (I knew offhand that ff+**eso injective on objects** functors are closed under pushout, but I confess I didn't check your link) | |
| Nov 6, 2021 at 2:46 | history | edited | varkor | CC BY-SA 4.0 |
added 202 characters in body
|
| Nov 6, 2021 at 2:40 | comment | added | varkor | @DavidRoberts: I've clarified my question and corrected a typo: the relevant fact is that fully faithful functors are closed under pushout, not pullback. | |
| Nov 6, 2021 at 2:38 | history | edited | varkor | CC BY-SA 4.0 |
added 66 characters in body
|
| Nov 6, 2021 at 2:08 | comment | added | David Roberts♦ | To clarify: what precisely is your 2-category 2-Cat? Also, that ff functors are closed under pullback seems like an instance of limits commuting with limits (since a ff functor can be characterised by a limit diagram, IIRC). | |
| Nov 6, 2021 at 0:19 | history | asked | varkor | CC BY-SA 4.0 |