Timeline for Can the objects of every concrete category themselves be realized as small categories?
Current License: CC BY-SA 2.5
6 events
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| Oct 19, 2009 at 22:41 | comment | added | Reid Barton | There's a subtlety for Grp also: the full sub-2-category of Cat on the one-object groupoids is not 2-equivalent to the category of groups, because the former has nontrivial natural transformations. The right way to fix this is to talk about pointed one-object groupoids, pointed functors and pointed natural transformations--again extra structure that must be preserved. | |
| Oct 19, 2009 at 7:40 | comment | added | Qiaochu Yuan | Hmm. I meant Ring, but I may have to take that back. It looks like the standard category-theoretic description of a ring is as a monoid object in Ab, so we need to require that the functors preserve the monoid structure. | |
| Oct 19, 2009 at 7:21 | comment | added | Reid Barton | How do you do it for Rng? | |
| Oct 19, 2009 at 7:08 | comment | added | Qiaochu Yuan | Darn. You probably understand why I asked this, though: this seems to be true of the standard concrete categories students are first introduced to, such as Grp, Rng, Top, ... are these categories characterized by a stronger property than concreteness? | |
| Oct 19, 2009 at 7:05 | vote | accept | Qiaochu Yuan | ||
| Oct 19, 2009 at 7:01 | history | answered | Reid Barton | CC BY-SA 2.5 |