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Stream: learning: questions

Topic: 2-density?

Martti Karvonen (Sep 25 2020 at 16:13):

Is anyone aware of a reference for density in two dimensions? I.e. definitions of dense 2-functors/subcategories and basic results concerning these? of course if everything is interpreted strictly one can just think in terms of dense $\mathcal{V}$-functors for $\mathcal{V}=Cat$, but I'm curious about the weaker case. Generalizing from my favorite definition to say that a bifunctor $D\colon J\to C$ is dense if for every $A$ and $B$ the canonical functor $C(A,B)\to J^{op},Cat$ is an equivalence seems straightforward, but if someone else has already worked out the basics I'd be happy to know so I'd get to actually using this concept faster.

Dan Doel (Sep 25 2020 at 17:09):

The canonical functor is a little off, right?

Martti Karvonen (Sep 25 2020 at 18:39):

Fixed now I think?

Dan Doel (Sep 25 2020 at 18:40):

Yeah, looks better.

Martti Karvonen (Sep 25 2020 at 18:41):

Maybe a bit dumb to call the functor D and the domain J (instead of the other way or smth), but yeah