strict category
- a strict category is a category together with the structure of a set on its collection of objects
- ==> objects can be compared for equality (not merely isomorphism)
- A weak category is a category without such structure
- A strict functor is a functor that preserves equality of objects:
F(x) = F(y) if x = y
skeletal category
- definition: a #strict category category is called skeletal if any two objects that are isomorphic are actually already equal