Functor sig_mor' sig_mor_as_sig := Build_Functor sig_mor' sig_mor_as_sig (fun x => exist _ x tt) (fun _ _ => idmap) (fun _ _ _ _ _ => idpath) (fun _ => idpath).
Require Import HoTT.Tactics Types.Forall Types.Sigma Basics.Trunc. Require Import Category.Core Functor.Core Category.Sigma.Core. Require Import Functor.Paths. Import Functor.Identity.FunctorIdentityNotations. Import Functor.Composition.Core.FunctorCompositionCoreNotations.