Timeline for What's special about the Simplex category?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 19, 2014 at 16:14 | comment | added | Mike Shulman | You mean the monadicity theorem? Yes, it always uses the analogous sort of "coequalizer", be it split or reflexive according to the theorem variant. | |
| Jun 18, 2014 at 17:25 | comment | added | Qiaochu Yuan | @Mike: cool. Presumably there's also something intelligent to say here about Barr-Beck-Lurie? | |
| Jun 18, 2014 at 15:42 | comment | added | Mike Shulman | There is something intelligent to say about finite products, and it has to do specifically with the degeneracy maps that you ignored. In ordinary category theory, reflexive coequalizers are sifted colimits, i.e. they commute with finite products. So the geometric realization of simplicial (not semisimplicial) objects commuting with finite products can be viewed as a categorification of that. | |
| Jun 17, 2014 at 0:27 | comment | added | Qiaochu Yuan | I totally neglected to mention the degeneracy maps here, but for the nerve they just come down to getting rid of the redundancies being caused by identity morphisms. | |
| Jun 16, 2014 at 21:04 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
added 261 characters in body
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| Jun 16, 2014 at 20:58 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |