Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
1 to 3 of 3
Just a quick question, in case anyone can tell me off hand (before I go scouring the literature): does the Gray tensor product make the category of strict 2-categories and pseudofunctors into a monoidal closed category? If so, is there a name for categories enriched in this category?
I haven’t seen this written down, I don’t think, or checked the details, but I’d be surprised if it weren’t monoidal and I’d be surprised if it were closed. For instance, since 1 is the unit for the Gray tensor product, you’d have a bijection between pseudofunctors $A\to B$ and pseudofunctors $1\to Hom(A,B)$. But the latter is not just an object of $Hom(A,B)$ but an automorphism in it coherently isomorphic to the identity. So I don’t see a natural candidate for $Hom(A,B)$.
Thanks for that, Mike. I thought I might need this to define some sort of 3-category of biprofunctors, but I don’t think it works. (It seems Biprof is best defined just as a subtricategory of Bicat.)
1 to 3 of 3