Timeline for Proving the impossibility of an embedding of categories
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 1, 2010 at 2:11 | vote | accept | Daniel Miller | ||
| Oct 1, 2010 at 1:58 | comment | added | David Roberts♦ | ah, you're right, and that's what I was thinking of anyway. :S stupid me.. | |
| Sep 30, 2010 at 15:21 | comment | added | Peter Arndt | Just about the terminology: The (oo,1)-category does not have fewer morphisms, the homotopy category does. | |
| Sep 30, 2010 at 7:44 | comment | added | David Roberts♦ | Of course there is, extra structure but the functors taken as examples (pi_n, H_n) descend to the (oo,1)-category, where there are fewer morphisms, and this is one point to consider when talking about faithful functors out of Top: they can't be invariant under homotopy | |
| Sep 30, 2010 at 7:40 | comment | added | Harry Gindi | (than just the homotopical structure, that is). | |
| Sep 30, 2010 at 7:39 | comment | added | Harry Gindi | Of course, saying that Top is only a presentation of the $(\infty,1)$-category of homotopy types is being a little bit unfair. Indeed, it has forgetful functors to the category of locales and the category of sets, which show that there's an even richer structure on actual topological spaces. | |
| Sep 30, 2010 at 6:14 | history | edited | David Roberts♦ | CC BY-SA 2.5 |
added 226 characters in body; added 84 characters in body
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| Sep 30, 2010 at 6:10 | comment | added | David Roberts♦ | I should just point out that given a functor Top-> Grp as you are looking for would make Top_cgwh a subcategory of Grp, but cartesian closedness and subcategories don't necessarily get along. | |
| Sep 30, 2010 at 3:24 | history | answered | David Roberts♦ | CC BY-SA 2.5 |