Lemma ismodulefun_comp {R} {M N P : module R} (f : R-mod(M,N)) (g : R-mod(N,P)) : ismodulefun (g ∘ f)%functions. Proof. exact (make_dirprod (isbinopfuncomp (modulefun_to_binopfun f) (modulefun_to_binopfun g)) (islinearfuncomp (modulefun_to_linearfun f) (modulefun_to_linearfun g))). Defined.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.Monoids.