Theorems · Theorem · group theory

MulSemiringActionHom.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} {R : Type u_10} [inst_3 : Semiring R] [inst_4 : MulSemiringAction M R] {S : Type u_12}
  [inst_5 : Semiring S] [inst_6 : MulSemiringAction N S] {T : Type u_14} [inst_7 : Semiring T]
  [inst_8 : MulSemiringAction P T] (g : S →ₑ+*[ψ] T) (f : R →ₑ+*[φ] S) [inst_9 : φ.CompTriple ψ χ] (x : R),
  (g.comp f) x = g (f x)

Defined in

Mathlib.GroupTheory.GroupAction.Hom

Cited by

2 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Quot.sound

Assumes

MonoidMonoidMonoidSemiringMulSemiringActionSemiringMulSemiringActionSemiringMulSemiringActionMonoidHom.CompTriple