fact: Definition Build_IsInitialMorphism_curried (A : D) (p : morphism C X (U A)) (Ap := CommaCategory.Build_object !X U tt A p) (m : forall (A' : D) (p' : morphism C X (U A')), morphism D A A') (H : forall (A' : D) (p' : morphism C X (U A')), U _1 (m A' p') o p = p') (H' : forall (A' : D) (p' : morphism C X (U A')) m', U _1 m' o p = p' -> m A' p' = m') : IsInitialMorphism Ap := Build_IsInitialMorphism A p (fun A' p' => Build_Contr _ (m A' p'; H A' p') (fun m' => path_sigma _ (m A' p'; H A' p') m' (H' A' p' m'.1 m'.2) (center _))).
imports: Category.Core Functor.Core Category.Dual Functor.Dual Category.Objects InitialTerminalCategory.Core InitialTerminalCategory.Functors Trunc Types.Sigma HoTT.Tactics Basics.Tactics