proposition: Lemma zero_eq_zero_opp (C:category) (a b:ob C) (o:ZeroObject C) : zeroMap' C^op (opp_ob b) (opp_ob a) (zero_opp C o) = opp_mor (zeroMap' C a b o).
proof: Proof. intros. try reflexivity. Abort. Definition HomPair {C:category} (a b:C) : [C^op,SET]. Proof. unshelve refine (makeFunctor_op _ _ _ _). - intro c. exact (Hom C c a × Hom C c b) % set. - simpl. intros c d f x. exact (pr1 x ∘ f ,, pr2 x ∘ f). - abstract (simpl; intro c; apply funextsec; intro x; apply dirprodeq; apply id_left) using _B_. - abstract (simpl; intros c d e f g; apply funextsec; intro x; apply dirprodeq; apply pathsinv0, assoc) using _C_. 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