Hello,
I'm quite new to Sage and until now I have read some basic tutorials on the categorical framework and on algebraic structures.
As I understood, categories are treated as an abstract class, to which one can add more concrete instances. I was wondering if there was a way to treat categories as more concrete objects, where you could explicitly define the objects and morphisms. I would expect that something like this could be implemented with a category of categories and specific parents. Along the same lines, one might ask how to handle the concepts of higher categories (or other properties to enrich a category).
In working with categorization, I would find a similar more concrete concept of category useful, in my case to implement the "Singular Coxeter Monoid" (insufficient karma to publish links, if you're interested look for "A singular Coxeter presentation"). I currently implement the object in question with a specific class that does not use predefined Parents.
So is there such a thing in Sage? Would it make sense for the Cat category to exist? Or are there fundamental problems that prevent a reasonable implementation of it?
