You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
Max New (Feb 01 2022 at 13:26):Is there a sensible notion of V-enriched sheaves? Looking on the nlab and Kelly (Basic Concepts of Enriched Category Theory) I only see things about enriched presheaves, which are fairly easy to define. I'm particularly interested in the simple case where V is thin
Reid Barton (Feb 01 2022 at 13:31):Certainly you can talk about sheaves of abelian groups, or simplicial sets, and so on. What do you mean by thin?
Zhen Lin Low (Feb 01 2022 at 13:49):Before even thinking about enriched sheaves I would be happy to have a good general definition of sheaves of X for a general category X.... but it seems difficult.
Max New (Feb 01 2022 at 17:23):Thin meaning the category is a preorder. Probably it is a frame/complete lattice. I'm looking for a good reference on V-valued sheaves oon a V-enriched category
Mike Shulman (Feb 01 2022 at 19:19):In general it's tricky to say what you would mean by a "Grothendieck topology" on an enriched category. But one thing you can do is talk about V-categories that are left-exact reflective subcategories of presheaf V-categories. The resulting notion of "V-topos" was studied a bit in Garner-Lack Lex colimits, and probably other places.