fact: Definition compose s d d' (gh : morphism d d') (g'h' : morphism s d) : morphism s d' := Build_morphism' s d' (gh.(g) o g'h'.(g)) (gh.(h) o g'h'.(h)) ((ap (fun m => m o s.(f)) (composition_of T _ _ _ _ _)) @ (associativity _ _ _ _ _ _ _ _) @ (ap (fun m => _ o m) g'h'.(p)) @ (associativity_sym _ _ _ _ _ _ _ _) @ (ap (fun m => m o _) gh.(p)) @ (associativity _ _ _ _ _ _ _ _) @ (ap (fun m => d'.(f) o m) (composition_of S _ _ _ _ _)^))%path ((ap (fun m => d'.(f) o m) (composition_of S _ _ _ _ _)) @ (associativity_sym _ _ _ _ _ _ _ _) @ (ap (fun m => m o _) gh.(p_sym)) @ (associativity _ _ _ _ _ _ _ _) @ (ap (fun m => _ o m) g'h'.(p_sym)) @ (associativity_sym _ _ _ _ _ _ _ _) @ (ap (fun m => m o s.(f)) (composition_of T _ _ _ _ _)^))%path.
imports: Functor.Core InitialTerminalCategory.Core InitialTerminalCategory.Functors Category.Strict HoTT.Basics HoTT.Types