Timeline for Bicategories in which the composition functors $\circ_{A, B, C}$ admit right adjoints
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 5 at 13:14 | comment | added | Paul Taylor | Reminds me of the interpolation property for continuous lattices (or posets or categories). | |
| Dec 4 at 10:44 | comment | added | varkor | I must admit I do not know of any examples beyond the one-object case! The condition seems rather strong, which suggests to me that there probably aren't many natural examples, but I believe there must be some (especially if Bénabou thought them interesting enough to study). I would hope that, if a reference exists, it also contains examples, but I would also be interested in an example even without a reference. | |
| Dec 4 at 10:31 | comment | added | Peter LeFanu Lumsdaine | Nice question. Do you know of any examples? Beyond the monoidal case, I can’t think of any at all, off the top of my head. E.g. even for typical bicategories of sup-complete posets, where composition preserves sups in each variable individually and hence has right adjoints on each side, it doesn’t preserve them as a functor of two variables together, if I’m not mistaken, so can’t have a total right adjoint. | |
| Dec 4 at 10:11 | history | asked | varkor | CC BY-SA 4.0 |