Timeline for Is there an operad that codifies groupoids?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 3, 2015 at 16:03 | comment | added | Zhen Lin | Ah, sorry, I was thinking of Barr-exactness + existence of coequalisers, which is what you need arbitrary intersections for. (Take the smallest congruence containing the relation corresponding to the parallel pair etc.) | |
| Oct 3, 2015 at 15:55 | comment | added | Todd Trimble | @ZhenLin Is this an example of what you mean? If $D$ is Barr-exact and coequalizers split in $D$, then for any monad $T$ the category of algebras $D^T$ is Barr-exact. I think it's just an easy argument using the fact that under the hypotheses, the monadic functor $U: D^T \to D$ preserves and reflects finite limits and coequalizers. | |
| Oct 3, 2015 at 14:29 | comment | added | Zhen Lin | Regarding the edit: is there an argument for Barr-exactness using only finite limits etc.? The only one I'm aware of uses the fact that $\mathbf{Set}$ has intersections of arbitrary collections of subobjects. | |
| Oct 3, 2015 at 13:45 | history | edited | Todd Trimble | CC BY-SA 3.0 |
addendum covering the multisorted case
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| Oct 2, 2015 at 4:31 | vote | accept | user40276 | ||
| Oct 1, 2015 at 20:16 | history | answered | Todd Trimble | CC BY-SA 3.0 |