Timeline for Conceptual reason that monadic functors create limits?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 22, 2020 at 0:49 | comment | added | Mike Shulman | Steve and I characterized the limits that lift to $\mathcal{F}$-categories of algebras and pseudo/lax/colax morphisms for a 2-monad in arxiv.org/abs/1104.2111 -- which was in fact the original purpose of introducing $\mathcal{F}$-categories. | |
| Feb 21, 2020 at 5:53 | comment | added | Tim Campion | @KevinCarlson Yeah, this business about assuming certain parts of the diagram preserve the limit is hard to put in a larger context. In the paper of Lack mentioned by john in his answer above, this pattern is repeated: he shows that $U: T-Alg_c \to C$ creates any comma objects where the appropriate leg is strong, etc. Maybe there's something to say about weighted $\mathcal F$-enriched limits... BTW does the forgetful functor from algebras for a 2-monad create even all flexible limits? | |
| Feb 18, 2020 at 6:35 | comment | added | Kevin Carlson | Well, PIE limits are well studied and have nice characterizations as in Bourke and Garner’s paper on flexible, semi flexible, and pie. However I’m not sure which legs of PIE limits are supposed to create limits...certainly one needs all the legs for products. More familiar is a result that flips roles around-the forgetful functor out of algebras for a 2-monad, with the pseudo morphisms, itself creates PIE limits! | |
| S Feb 17, 2020 at 19:19 | history | answered | Tim Campion | CC BY-SA 4.0 | |
| S Feb 17, 2020 at 19:19 | history | made wiki | Post Made Community Wiki by Tim Campion |