Theorems · Theorem · group theory

MulActionHom.comp_assoc

∀ {M : Type u_2} {N : Type u_3} {P : Type u_4} {φ : M → N} {ψ : N → P} {χ : M → P} {X : Type u_5} [inst : SMul M X]
  {Y : Type u_6} [inst_1 : SMul N Y] {Z : Type u_7} [inst_2 : SMul P Z] {Q : Type u_8} {T : Type u_9}
  [inst_3 : SMul Q T] {η : P → Q} {θ : M → Q} {ζ : N → Q} (h : Z →ₑ[η] T) (g : Y →ₑ[ψ] Z) (f : X →ₑ[φ] Y)
  [inst_4 : CompTriple φ ψ χ] [inst_5 : CompTriple χ η θ] [inst_6 : CompTriple ψ η ζ] [inst_7 : CompTriple φ 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 13 from the axioms · uses Quot.sound

Assumes

SMulSMulSMulSMulCompTripleCompTripleCompTripleCompTriple