`(IsTerminalCategory one) (HT : P one) : IsTerminalObject (sub_pre_cat P HF) (one; HT). Proof. typeclasses eauto. Defined.
Require Import Category.Objects InitialTerminalCategory.Core InitialTerminalCategory.Functors Functor.Core Category.Strict Functor.Paths. Require Import Functor.Identity Functor.Composition.Core Functor.Composition.Laws.