Theorems · Definition · group theory

Function.Injective.mulDistribMulAction

{M : Type u_2} →
  {A : Type u_3} →
    {B : Type u_4} →
      [inst : Monoid M] →
        [inst_1 : Monoid A] →
          [inst_2 : MulDistribMulAction M A] →
            [inst_3 : Monoid B] →
              [inst_4 : SMul M B] →
                (f : B →* A) →
                  Function.Injective ⇑f → (∀ (c : M) (x : B), f (c • x) = c • f x) → MulDistribMulAction M B

Pullback a multiplicative distributive multiplicative action along an injective monoid homomorphism.

Defined in

Mathlib.Algebra.Group.Action.Basic

Cited by

0 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext

Assumes

MonoidMonoidMulDistribMulActionMonoidSMul