Theorems · Theorem · group theory

DistribMulActionHom.comp_assoc

∀ {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] {Q : Type u_11} {D : Type u_12} [inst_9 : Monoid Q] [inst_10 : AddMonoid D]
  [inst_11 : DistribMulAction Q D] {η : P →* Q} {θ : M →* Q} {ζ : N →* Q} (h : C →ₑ+[η] D) (g : B →ₑ+[ψ] C)
  (f : A →ₑ+[φ] B) [inst_12 : φ.CompTriple ψ χ] [inst_13 : χ.CompTriple η θ] [inst_14 : ψ.CompTriple η ζ]
  [inst_15 : φ.CompTriple ζ θ], h.comp (g.comp f) = (h.comp g).comp f

Defined in

Mathlib.GroupTheory.GroupAction.Hom

Cited by

0 results in Mathlib

Foundations

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

Assumes

MonoidMonoidMonoidAddMonoidDistribMulActionAddMonoidDistribMulActionAddMonoidDistribMulActionMonoidAddMonoidDistribMulActionMonoidHom.CompTripleMonoidHom.CompTripleMonoidHom.CompTripleMonoidHom.CompTriple