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Finite categories?


As part of a project on geometry of moduli of curves ('stacky fans') I'm trying to implement `categories with finitely many objects and finitely many morphisms'. I've started creating a class FiniteCat, but I can't decide whether it should be a child of DiGraph (where I add extra data of composition) , or of Category, using the existing machinery around that.

For context, I'm going to start with creating a FiniteCat from a lattice/poset (with maybe a couple of hundred vertices), then adding in a few more interesting (auto)morphisms). The main purpose is that I want to look at (pre)sheaves on these categories, check whether certain collections of data define sections of these presheaves, and perform basic operations on them.

Any suggestions would be very welcome .

Thanks, David Holmes