C-Sets

[olynch]

We can write out the theory of a copresheaf on a given schema by writing the schema as an extension of the theory of categories, writing out the theory of a copresheaf as an extension of categories, and then taking their pushout.

We should then have C-Sets be models of this theory, and then the API for C-Sets can come from the generic API for a model of a theory.

This requires some extensions to what it means to be a model, however.

• If we want to use integers as ids, then we need the checkvalidity method to also take in the type arguments, so that checking if a part is in a C-Set can be a typecheck of i::Elem(E), for instance, which checks if i is in the range of edges for a graph.
• There should be optional methods which return all of the elements of a certain type, or which return all of the generators of a certain type. This is not always possible for all models, but would be useful for some models.

[jpfairbanks]

Is this:

There should be optional methods which return all of the elements of a certain type, or which return all of the generators of a certain type. This is not always possible for all models, but would be useful for some models.

feature necessary to get the parts(G, :V) api to work?

[olynch]

Yeah, exactly