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.
I added some examples of virtual double categories that do not have composites described in Crutwell-Shulman.
@Mike Shulman, on this page you said virtual double categories can be defined as
a generalized multicategory, in the sense of Hermida, Cruttwell-Shulman, and others, relative to the monad T on graphs-internal-to-Cat whose algebras are double categories
did you mean “categories internal to Grph” rather than “graphs internal to Cat”? That seems to be how y’all defined it in Cruttwell-Shulman. I have a suspicion they turn out to be the same thing, but when you define the monad it is easier to think of it as categories internal to Grph because the monad is a lifting of the free category monad on Grph.
They are the same thing. I find it easier to think of graphs internal to Cat, because then the monad is just the special case of the free internal-category monad in the topos of graphs.
1 to 3 of 3