Timeline for Any cocomplete category with a dense small full subcategory is complete?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Feb 6, 2016 at 7:43 | comment | added | Bruno Stonek | For future readers, I'd like to point out a reference to this fact: corollary 6.5, "A survey of totality for enriched and ordinary categories", by Max Kelly, where it is worked out in the enriched context. | |
| Jul 11, 2012 at 21:28 | comment | added | Mike Shulman | Like I said: close. (-: | |
| Jul 11, 2012 at 20:37 | comment | added | David Carchedi | @Mike: Well, this is basically contained in his proof. You just have compose with the geometric morphism $(i_*,i^*),$ where $i:D \hookrightarrow C$ is the inclusion. Since $i$ is full and faithful, so is $i_*.$ | |
| Nov 11, 2010 at 3:39 | comment | added | Mike Shulman | Not exactly; it looks to me like he proved that the embedding of C into the presheaf category of its small dense subcategory D has a left adjoint, rather than that the embedding of C into its own presheaf category has a left adjoint. Close, though. | |
| Nov 10, 2010 at 23:40 | comment | added | Martin Brandenburg | Well this is included in Sasha's proof, right? | |
| Nov 10, 2010 at 21:25 | history | answered | Mike Shulman | CC BY-SA 2.5 |