fact: Definition identity : Pseudofunctor cat := Build_Pseudofunctor cat (fun C => C.1) (fun _ _ F => F) (fun _ _ _ _ _ => reflexivity _) (fun _ => reflexivity _) (fun x y z w => @identity_associativity x.1 y.1 z.1 w.1) (fun x y => @identity_left_identity x.1 y.1) (fun x y => @identity_right_identity x.1 y.1).
imports: FunctorCategory.Morphisms Category.Core Functor.Core NaturalTransformation.Isomorphisms NaturalTransformation.Paths Cat.Core Pseudofunctor.Core PathGroupoids