proposition: Lemma HomPairOp {B C : category} (F G : [B, C]) : z_iso (HomPair (functorOp F) (functorOp G) □ functorOp') (HomPair (opp_ob F) (opp_ob G)).
proof: Proof. unshelve refine (makeNatiso _ _). { intros H. apply hset_equiv_z_iso. apply weqdirprodf; exact (invweq (isomorphismOnMor functorOpIso H _)). } { abstract (intros H J p; apply funextsec; intro w; apply dirprodeq; ( apply nat_trans_eq; [ apply homset_property | reflexivity ] )). } Defined.
imports: UniMath.Foundations.Preamble UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.RepresentableFunctors.Bifunctor UniMath.CategoryTheory.RepresentableFunctors.Precategories UniMath.MoreFoundations.Tactics