Theorems · Theorem · group theory

DistribMulActionHom.comp_apply

∀ {M : Type u_1} [inst : Monoid M] {N : Type u_2} [inst_1 : Monoid N] {P : Type u_3} [inst_2 : Monoid P] {φ : M →* N}
  {ψ : N →* P} {χ : M →* P} {A : Type u_4} [inst_3 : AddMonoid A] [inst_4 : DistribMulAction M A] {B : Type u_5}
  [inst_5 : AddMonoid B] [inst_6 : DistribMulAction N B] {C : Type u_7} [inst_7 : AddMonoid C]
  [inst_8 : DistribMulAction P C] (g : B →ₑ+[ψ] C) (f : A →ₑ+[φ] B) [inst_9 : φ.CompTriple ψ χ] (x : A),
  (g.comp f) x = g (f x)

Defined in

Mathlib.GroupTheory.GroupAction.Hom

Cited by

2 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Quot.sound

Assumes

MonoidMonoidMonoidAddMonoidDistribMulActionAddMonoidDistribMulActionAddMonoidDistribMulActionMonoidHom.CompTriple