Theorems · Definition · group theory

Function.Injective.distribSMul

{M : Type u_1} →
  {A : Type u_7} →
    {B : Type u_9} →
      [inst : AddZeroClass A] →
        [inst_1 : DistribSMul M A] →
          [inst_2 : AddZeroClass B] →
            [inst_3 : SMul M B] →
              (f : B →+ A) → Function.Injective ⇑f → (∀ (c : M) (x : B), f (c • x) = c • f x) → DistribSMul M B

Pullback a distributive scalar multiplication along an injective additive monoid homomorphism. See note [reducible non-instances].

Defined in

Mathlib.Algebra.GroupWithZero.Action.Defs

Cited by

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Foundations

Depth 15 from the axioms · uses propext

Assumes

AddZeroClassDistribSMulAddZeroClassSMul