Timeline for The main theorems of category theory and their applications
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jan 1, 2012 at 5:40 | history | edited | Ed Dean | CC BY-SA 3.0 |
typo
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| Dec 16, 2011 at 8:18 | comment | added | Andrej Bauer | @Paul: in category theory constructions have their own value, they need not always be accompanied by mind-blowing theorems. The constructions can already be mind-blowing. | |
| Dec 15, 2011 at 5:54 | comment | added | Anton Fetisov | @David: Yes, of course. I just didn't feel like discussing technical conditions. The existence of such internal language is, in my opinion, a prominent categorical fact by itself. It is completely non-obvious. The study of semantics for this language also takes many pages and is categorical in nature. The problems of set theory are of little importance here. | |
| Dec 15, 2011 at 3:59 | comment | added | Paul Siegel | This sounds like a nice application of the existence of certain categories, but is there a particular theorem or set of theorems in category theory that is relevant here? It sounds like the hard work here might really be in logic or set theory. | |
| Dec 15, 2011 at 2:04 | comment | added | David Roberts♦ | @Toby - Giraud's theorem? As opposed to saying (as I implicitly did) 'A [topos equivalent to a category of sheaves] is a category of sheaves'. :) | |
| Dec 15, 2011 at 1:56 | comment | added | Toby Bartels | More explicitly, any topos that has all small (not just finitary) coproducts and satisfies a size condition is a category of sheaves. | |
| Dec 15, 2011 at 0:57 | comment | added | David Roberts♦ | Any Grothendieck topos is a category of sheaves. | |
| Dec 15, 2011 at 0:42 | history | answered | Anton Fetisov | CC BY-SA 3.0 |