Timeline for Natural ways to make a functor adjoint
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 14 at 19:50 | answer | added | Tom Leinster | timeline score: 4 | |
| Jan 14 at 15:46 | comment | added | Paul Taylor | One would expect this to be formulated as "freely adding a right adjoint", so that there is a square of functors ${\mathcal C}\to{\widehat{\mathcal C}}$ that is universal in some 2-categorical sense, I think "pseudo", ie "up to unique isomorphism. I don't think this can be achieved by localisation. If $\mathcal C$ is to be included in ${\widehat{\mathcal C}}$, whilst the latter also has values for the right adjoint, then ${\widehat{\mathcal C}}$ would have more objects than $\mathcal C$, whereas localisation is essentially surjective. | |
| Jan 14 at 0:12 | answer | added | Nick Hu | timeline score: 10 | |
| Jan 12 at 7:40 | comment | added | varkor | If your categories are small and Cauchy-complete, a natural choice is to take the presheaf construction. (Cauchy-completeness is necessary because $F$ is only recoverable up to Cauchy completion.) | |
| Jan 12 at 0:41 | history | asked | Student | CC BY-SA 4.0 |