Timeline for Can skeleta simplify category theory?
Current License: CC BY-SA 2.5
9 events
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| S Feb 26, 2018 at 16:51 | history | rollback | Mike Shulman |
Rollback to Revision 1 - Edit approval overridden by post owner or moderator
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| Feb 26, 2018 at 6:55 | history | suggested | Mike Pierce | CC BY-SA 3.0 |
Added a link, and mathjaxxed
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| Feb 26, 2018 at 1:02 | review | Suggested edits | |||
| S Feb 26, 2018 at 16:51 | |||||
| Jun 19, 2010 at 4:42 | comment | added | Mike Shulman | I suppose you could think of that as somewhat analogous. I don't think it would be especially helpful, though, for the reasons mentioned above -- passing to skeletal categories rarely makes things any simpler. | |
| Jun 18, 2010 at 13:42 | comment | added | Sean Tilson | it seems like there might be an analogy between CW-complexes as skeletal categories, topologoical spaces as categories, the result that an equivalence is an isomorphism btwn skeletal categories as Whitehead's thm, and that every category is equivalent to a skeletal one as the fact that every space has the htopy type of a CW-complex. Is this relevant, completely off, or have any accuracy? | |
| Jan 15, 2010 at 4:32 | comment | added | Mike Shulman | Yes... but if you then want to relate your unique-on-the-nose object back to the original category you were working in (which presumably you want to do), then there are lots of ways to do it and no canonical choice. So the uniqueness only exists in an artificial world, that has little to do with the real one. | |
| Jan 14, 2010 at 13:41 | comment | added | Andrea Ferretti | I should only add that in the last example, one can see the product of A and B as a final object in the category of triples (P, f, g) where f is in Hom(P, A) and g in Hom (P, B). If you take a skeleton of THIS category, then the object should be unique on the nose, if I'm not wrong. | |
| Jan 14, 2010 at 13:35 | vote | accept | Andrea Ferretti | ||
| Jan 13, 2010 at 19:25 | history | answered | Mike Shulman | CC BY-SA 2.5 |