Timeline for Cobordism categories that don't involve manifolds
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Mar 29, 2011 at 15:20 | comment | added | Todd Trimble | I'll need some time to think about your question, Dylan. In the meantime, I've added some possibly more meaningful observations to my answer. | |
| Mar 29, 2011 at 15:19 | history | edited | Todd Trimble | CC BY-SA 2.5 |
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| Mar 29, 2011 at 3:32 | comment | added | Dylan Wilson | Thanks! Does the notion of bordism equivalence that this gives have any use for common problems? Like, in some (specific) non-geometric category, what properties of a map are bordism invariant in this case that we care about? | |
| Mar 27, 2011 at 6:23 | comment | added | Todd Trimble | @Qiaochu: yes. Either is a simple example, but I thought the arrow category was simpler. My guess is that it's well-known. | |
| Mar 27, 2011 at 5:47 | comment | added | Qiaochu Yuan | Isn't that a subcategory of the cospan category anyway? (Those are just the cospans with $Y = 0$, right?) | |
| Mar 27, 2011 at 5:38 | comment | added | Todd Trimble | Well, heck, why don't I just take the arrow category instead and define $\partial (f: X \to Y) = (0 \to X)$? That works too. I guess the reason is that I was thinking also of composition of cobordisms, and how that generalizes to taking pushouts of cospans. | |
| Mar 27, 2011 at 3:49 | history | answered | Todd Trimble | CC BY-SA 2.5 |