Timeline for What properties do "large topoi" share with actual topoi?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 30, 2015 at 11:27 | history | edited | Zhen Lin | CC BY-SA 3.0 |
added 6 characters in body
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| Nov 28, 2013 at 23:09 | vote | accept | David Carchedi | ||
| Nov 28, 2013 at 23:09 | comment | added | David Carchedi | Ah- well, I suppose one needs the caveat that $\mathcal{A}$ is also locally small, which a big group is not. | |
| Nov 28, 2013 at 23:09 | comment | added | Zhen Lin | The Elephant has a few things to say about pretoposes scattered here and there, but you can probably find more information by looking up lextensive and effective regular categories separately. | |
| Nov 28, 2013 at 23:07 | comment | added | Zhen Lin | That's certainly not true. As I said, $[\mathcal{A}^\mathrm{op}, \mathbf{Set}]$ is locally small when $\mathcal{A}$ is a "big group". Indeed, the hom-sets are even subsets of the hom-sets of the underlying sets! | |
| Nov 28, 2013 at 23:04 | comment | added | David Carchedi | By the way, in light of Todd's answere here: mathoverflow.net/questions/24540/… it seems $[\mathcal{A}^{op},\mathbf{Set}]$ is only locally small if $\mathcal{A}$ is essentially small. | |
| Nov 28, 2013 at 22:59 | comment | added | David Carchedi | Thanks Zhen for the nice answer. Could you perhaps recommend a good reference? | |
| Nov 28, 2013 at 22:01 | history | answered | Zhen Lin | CC BY-SA 3.0 |