`{@IsInitialCategory zero} (F : Functor C zero) : IsInitialCategory C := fun P x => initial_category_ind P (F x). Global Instance trunc_terminal_category `{@IsTerminalCategory one H1 H2} : Contr (Functor C one). Proof. refine (Build_Contr _ (to_terminal C) _). intros. exact (center _). Defined.
Require Import Category.Core Functor.Core Functor.Paths. Require Import InitialTerminalCategory.Core. Require Import NatCategory. Require Import HoTT.Basics.