∀ (k G : Type u_1) [inst : CommRing k] [inst_1 : Group G] {X Y Z : Rep k G} (f : X ⟶ Y) (g : Y ⟶ Z),
  ModuleCat.ofHom
      (LinearMap.codRestrict Z.ρ.invariants
        (ModuleCat.Hom.hom (CategoryTheory.CategoryStruct.comp f g).hom ∘ₗ X.ρ.invariants.subtype) ⋯) =
    CategoryTheory.CategoryStruct.comp
      (ModuleCat.ofHom (LinearMap.codRestrict Y.ρ.invariants (ModuleCat.Hom.hom f.hom ∘ₗ X.ρ.invariants.subtype) ⋯))
      (ModuleCat.ofHom (LinearMap.codRestrict Z.ρ.invariants (ModuleCat.Hom.hom g.hom ∘ₗ Y.ρ.invariants.subtype) ⋯))