proposition: Lemma Quotcategory_comp_linear {x y z : ob PA} (f : PA⟦x, y⟧) (g : PA⟦y, z⟧) : Quotcategory_comp (to_quot_mor f) (to_quot_mor g) = to_quot_mor (f · g).
proof: Proof. unfold to_quot_mor. unfold Quotcategory_comp. apply pathsinv0. use (pr2 (pr1 (Quotcategory_comp_iscontr (setquotpr (binopeqrel_subgr_eqrel (PAS x y)) f) (setquotpr (binopeqrel_subgr_eqrel (PAS y z)) g)))). - apply idpath. - apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels