A `{HasEquivs A} (x y : A) : IsInitial x -> IsInitial y -> x $<~> y. Proof. intros inx iny. srapply (cate_adjointify (inx y).1 (iny x).1). 1: exact (((iny _).2 _)^$ $@ (iny _).2 _). 1: exact (((inx _).2 _)^$ $@ (inx _).2 _). Defined.
Require Import Basics.Utf8 Basics.Overture Basics.Tactics Basics.Equivalences. Require Import WildCat.Core. Require Import WildCat.Opposite.