Timeline for Notation for "the" left adjoint functor
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 29, 2020 at 22:56 | comment | added | LSpice | @Adrien, how about ${^{\text L}F}$ and $F^{\text R}$? (EDIT: Ah, this is basically @FredRohrer's answer.) | |
| Apr 29, 2020 at 20:16 | answer | added | Henning Krause | timeline score: 5 | |
| Feb 1, 2020 at 21:13 | history | became hot network question | |||
| Feb 1, 2020 at 20:35 | vote | accept | Martin Brandenburg | ||
| Feb 1, 2020 at 20:32 | comment | added | Martin Brandenburg | @TimPorter I completely agree. But sometimes the letters $U,L,R$ are already taken, or when no other functor is in the context, it is very common to name the functor $F$. By the way, Borceux calls $F$ the right and $G$ the left adjoint, yikes! | |
| Feb 1, 2020 at 18:13 | answer | added | Fred Rohrer | timeline score: 19 | |
| Feb 1, 2020 at 17:19 | comment | added | Tim Porter | I think the use of $F$ for a start is problematic. Often $F$ is the left adjoint as it is often used for 'free' with $U$ or similar standing for 'underlying'. Different contexts require different notation but I have used $L$ for the left adjoint and $R$ for the right when discussing adjoint functors when teaching category theory. It might help if you gave more idea of the context in which you are wanting this. | |
| Feb 1, 2020 at 17:00 | comment | added | Oscar Cunningham | You could write it as a formula using limits: $d\mapsto \lim(\pi:d/F\to C)$. | |
| Feb 1, 2020 at 15:59 | comment | added | Martin Brandenburg | @Adrien Thanks. Can you give an example of a book where it is used? | |
| Feb 1, 2020 at 13:06 | comment | added | Adrien | I've no idea how widely used it is, but I like $F^L$ for the left adjoint and $F^R$ for the right one. | |
| Feb 1, 2020 at 13:01 | history | asked | Martin Brandenburg | CC BY-SA 4.0 |