IIUC, category theory only applies to immutable objects, and mutability is modelled within that using e.g. functors, monads. Is that true? If so, why doesn't category theory include immutability? Has no-one got round to adding that, or is it impossible?
I'm asking because I've never seen category theory applied to, or discussed in the context of, imperative code or languages, and I want to know if it can be.