fact: Definition sub_pre_cat : PreCategory := @Build_PreCategory { C : PreCategory | P C } (fun C D => Functor C.1 D.1) (fun C => identity C.1) (fun _ _ _ F G => F o G) (fun _ _ _ _ _ _ _ => associativity _ _ _) (fun _ _ _ => left_identity _) (fun _ _ _ => right_identity _) (fun s d => HF s.2 d.2).
imports: Category.Objects InitialTerminalCategory.Core InitialTerminalCategory.Functors Functor.Core Category.Strict Functor.Paths Functor.Identity Functor.Composition.Core Functor.Composition.Laws