Timeline for Category whose morphisms are commutative monoids but not enriched
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 2 at 19:08 | comment | added | varkor | @FJ: in your example(s), does composition preserve addition on one side, but not both? Or does it not preserve addition on either side? | |
| Dec 23, 2022 at 8:22 | review | Close votes | |||
| Dec 28, 2022 at 3:06 | |||||
| Dec 22, 2022 at 20:03 | comment | added | Dmitri Pavlov | @FJ: Since you have a concrete category in mind, to provide a meaningful answer you really need to spell out the details of your category. It is not possible to gather what kind of structure you have just from the vague descriptions we have so far. | |
| Dec 22, 2022 at 17:51 | comment | added | Fernando Muro | @TimCampion ooooops… | |
| Dec 22, 2022 at 16:59 | comment | added | Tim Campion | @FernandoMuro Or at least -- any nonempty set! | |
| Dec 22, 2022 at 13:13 | comment | added | Fernando Muro | Any category can be endowed with such a structure since any set can be made a commutative monoid. | |
| Dec 22, 2022 at 11:04 | comment | added | F J | Roughly speaking (not very precise), an object $X$ is a measurable space. $\text{Mor}(X,Y)$ are like random variables which can be added. Compositions are defined in a more involved way but the key point is that they are not distributive w.r.t. the addition. To study relations with other categories with similar structures, I want to look at functors that preserve the monoid structure. I would like to know if there is already some theory on such categories. | |
| Dec 22, 2022 at 10:58 | comment | added | Peter LeFanu Lumsdaine | I guess the specific example you came across is too specialised to describe here — but can you give some “toy example” of such a situation? | |
| Dec 22, 2022 at 9:38 | history | asked | F J | CC BY-SA 4.0 |