Timeline for On the category of virtual species
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 21, 2013 at 16:07 | comment | added | Jacques Carette | @Todd: Would you mind if I asked you a few more questions about this? Email might be best [carette at mcmaster dot ca]. | |
| Mar 19, 2013 at 12:13 | vote | accept | Jacques Carette | ||
| Mar 19, 2013 at 12:13 | comment | added | Jacques Carette | Thanks Todd, that makes sense (the simpler construction). The "if you like" comes close to making sense (to me) too... more learning to do. And I would also really like to know why this was downvoted! | |
| Mar 19, 2013 at 11:19 | comment | added | Todd Trimble | Also: would the downvoter care to explain why he/she downvoted both the question and this answer? | |
| Mar 19, 2013 at 11:17 | comment | added | Todd Trimble | If you like, it's the free compact closed category generated from the symmetric monoidal groupoid of finite sets. | |
| Mar 19, 2013 at 11:13 | comment | added | Todd Trimble | Jacques, sorry -- I was just trying to save space in that (perhaps needlessly fancy) description, and should have said "diffeomorphism classes". Anyway, another description is that if $A$ and $B$ are multisets of +'s and -'s, then a morphism $A \to B$ is a partition of the multiset $-A + B$ into two-element subsets consisting of a + and a - in each subset (a directed edge from the - to the +) together with possible free-floating loops. Also, I don't think anyone would have written gone through the tortile category construction for this case, because that's like nuking a fly with a bomb. (...) | |
| Mar 19, 2013 at 3:04 | comment | added | Jacques Carette | My mathematical education unfortunately did not cover cobordisms (but I otherwise understand the 'expansion' of the definition). What I don't understand is why the morphisms involve 1-manifolds. Is this somehow equivalent to the more 'discrete' sounding case of tangles on ribbons from Traced Monoidal Categories? Or are you using 1-manifold in an $\mathbb{R}$-free way, in the same way that homotopy-type-theorists define $S^1$? Would anyone have ever written down the details of applying the tortile category construction to FinSet? | |
| Mar 19, 2013 at 0:24 | history | answered | Todd Trimble | CC BY-SA 3.0 |