Timeline for Why is a monoid with closed symmetric monoidal module category commutative?
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 28, 2013 at 12:32 | answer | added | Buschi Sergio | timeline score: 0 | |
| Jul 9, 2011 at 16:56 | comment | added | Nacho Lopez | This seems to be the old result of Kock on commutative monads (the monad here being $(A\otimes−)$). What is true is that TFAE: 1. Mod(A) is closed (resp monoidal) and the free A-module adjunction $F\dashv U:\mathbf{Mod}(A)\to\mathcal{V}$ is a closed adjunction (resp. monoidal adjunction). 2. A is commutative. | |
| Feb 11, 2010 at 19:45 | comment | added | Peter Arndt | That is how I understood it - Tyler's newly edited answer gives now an easy counterexample to my original statement (the former one used things I didn't know). And Clark's proof works and tells me what I wanted to know. | |
| Feb 11, 2010 at 1:23 | comment | added | Tom Leinster | OK, let's see if I have this right. Tyler's "no" and Clark's "yes" are both correct. Tyler's "no" answers the question posed. Clark's "yes" answers the same question but under the assumption of a (sensible) extra hypothesis. Right? | |
| Feb 10, 2010 at 18:42 | vote | accept | Peter Arndt | ||
| Feb 10, 2010 at 17:17 | answer | added | Victor Ostrik | timeline score: 6 | |
| Feb 10, 2010 at 11:43 | comment | added | Clark Barwick | Tom Leinster - one does have to require that the natural right action of the ambient category is compatible with the monoidal structure on the category of modules, but that's it. | |
| Feb 10, 2010 at 11:01 | comment | added | Tom Leinster | I find this a really strange statement. Are the monoidal structure and the symmetry on A-Mod really not required to bear any kind of relationship to the monoidal structure and symmetry on your original category? | |
| Feb 10, 2010 at 6:26 | answer | added | Tyler Lawson | timeline score: 4 | |
| Feb 10, 2010 at 1:43 | answer | added | Clark Barwick | timeline score: 12 | |
| Feb 9, 2010 at 21:13 | history | asked | Peter Arndt | CC BY-SA 2.5 |