Re “I’m not fully sold on category theory as a mathematical tool”, if someone (e.g. me) were to take the category you’ve outlined and run with it, in the sense of establishing its general structure and special features, could you be convinced? Are there questions that you have about this category that you currently are only able to answer by brute force computation from the definitions of the objects and morphisms as you’ve given them? More generally, are there variants of this category that you’ve considered that it might be useful to study in parallel?
For the moment, I’m going to be trying to resolve practical questions of model splintering, and then I’ll see if this formalism turns out to be useful for them.
Re “I’m not fully sold on category theory as a mathematical tool”, if someone (e.g. me) were to take the category you’ve outlined and run with it, in the sense of establishing its general structure and special features, could you be convinced? Are there questions that you have about this category that you currently are only able to answer by brute force computation from the definitions of the objects and morphisms as you’ve given them? More generally, are there variants of this category that you’ve considered that it might be useful to study in parallel?
For the moment, I’m going to be trying to resolve practical questions of model splintering, and then I’ll see if this formalism turns out to be useful for them.