Timeline for A fibration equivalent to having a terminal object
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 3, 2022 at 1:26 | history | edited | Alec Rhea | CC BY-SA 4.0 |
was correct the first time
|
| Feb 1, 2022 at 22:46 | history | edited | Alec Rhea | CC BY-SA 4.0 |
construction still doesn't work right
|
| Feb 1, 2022 at 22:26 | history | edited | Alec Rhea | CC BY-SA 4.0 |
deleted 4 characters in body
|
| Feb 1, 2022 at 22:18 | history | edited | Alec Rhea | CC BY-SA 4.0 |
fixed fibration to actually yield all pullbacks
|
| Feb 1, 2022 at 15:26 | history | became hot network question | |||
| Feb 1, 2022 at 10:13 | history | edited | Alec Rhea | CC BY-SA 4.0 |
realized construction doesn't yield all pullbacks
|
| Feb 1, 2022 at 9:59 | history | edited | Alec Rhea | CC BY-SA 4.0 |
fixed the codomain fibration to give all pullbacks
|
| Feb 1, 2022 at 9:31 | history | edited | Alec Rhea | CC BY-SA 4.0 |
corrected error thanks to Alexander; the codomain functor being a fibration only gives finite pullbacks
|
| Feb 1, 2022 at 9:26 | comment | added | Alec Rhea | @AndrejBauer Hmm, so we would need to define the category of sinks in a category, then the obvious codomain functor from the sink category down to the original one -- if this functor is a fibration, then the category has all pullbacks and not just binary ones. Does this sound correct? | |
| Feb 1, 2022 at 9:21 | comment | added | Alec Rhea | But now I'm wondering if the fibrational characterization of pullbacks only holds for binary ones; I think I need to be more careful here. | |
| Feb 1, 2022 at 9:20 | comment | added | Alec Rhea | @AlexanderCampbell Ah, I see the confusion thanks to Andrej -- when I say that a category 'has pullbacks', I mean arbitrary ones not binary ones. (limits of diagrams shaped like arbitrarily many points each with a unique morphism to some specific point) | |
| Feb 1, 2022 at 9:05 | comment | added | Andrej Bauer | @AlecRhea: You should have an opinion poll that finds out how many people think that "pullback" means the limit of $\bullet \to \bullet \leftarrow \bullet$. | |
| Feb 1, 2022 at 8:10 | comment | added | Alec Rhea | @AlexanderCampbell A category is complete iff it has all products and equalizers iff it has all pullbacks and a terminal object. For finite completeness we would only require finite pullbacks and a terminal object. | |
| Feb 1, 2022 at 8:08 | vote | accept | Alec Rhea | ||
| Feb 1, 2022 at 7:46 | comment | added | Alexander Campbell | N.B. A category has pullbacks and a terminal object iff it is finitely complete. | |
| Feb 1, 2022 at 7:44 | answer | added | Alexander Campbell | timeline score: 10 | |
| Feb 1, 2022 at 7:21 | history | asked | Alec Rhea | CC BY-SA 4.0 |