Functor sig_obj sig_obj_as_sig := Build_Functor sig_obj sig_obj_as_sig (fun x => x) (fun _ _ m => exist _ m tt) (fun _ _ _ _ _ => idpath) (fun _ => idpath).
Require Import HoTT.Basics HoTT.Types. Require Import Category.Core Functor.Core Category.Sigma.Core. Require Import Functor.Paths. Import Functor.Identity.FunctorIdentityNotations. Import Functor.Composition.Core.FunctorCompositionCoreNotations.