skeletal category

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