Timeline for Correspondence between operads and monads requires tensor distribute over coproduct?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 20 at 0:00 | comment | added | David White | This paper of Michael Ching's from 2005 is relevant: arxiv.org/abs/math/0510490 | |
| May 15, 2015 at 18:59 | answer | added | Dmitri Pavlov | timeline score: 5 | |
| Dec 26, 2013 at 2:14 | vote | accept | ziggurism | ||
| Dec 26, 2013 at 2:13 | comment | added | ziggurism | Thank you for clarifying, gentlemen. I had thought requiring monoidal product to preserve coproducts would be an unusual requirement, which is why I had to ask. I somehow forgot that this was implied by closedness of the monoidal product, which is a natural for enrichment categories. So obvious in hindsight... thanks again! | |
| Dec 25, 2013 at 20:59 | comment | added | Peter May | Quite right, Tom. I did mention taking V to be closed on page 3 of the paper Joe cites and Fernando rightly points out that that fixes everything. I should have assumed that or the distributivity explicitly (as I'm sure I did elsewhere). In all of my applications, V has been closed. | |
| Dec 25, 2013 at 17:09 | comment | added | Tom Leinster | I've certainly always assumed this distributivity, and I'm pretty sure it (or something close to it) is needed. If it's not mentioned in that paper of Peter May's, it must just have been a slip on his part. | |
| Dec 25, 2013 at 9:52 | comment | added | Fernando Muro | You're completely correct. I've also found such things. The point is that people often consider operads in closed symmetric monoidal categories, hence $\otimes$ preserves $\coprod$. I had wondered about the insistence on closedness. First I thought it was only to define endomorphism operads, but it also solves more subtle problems like the one you point out. | |
| Dec 25, 2013 at 8:39 | answer | added | Dan Petersen | timeline score: 5 | |
| Dec 25, 2013 at 7:18 | history | asked | ziggurism | CC BY-SA 3.0 |