Theorems · Definition · group theory

Function.Injective.semigroupWithZero

{M₀ : Type u_1} →
  {M₀' : Type u_3} →
    [inst : Zero M₀'] →
      [inst_1 : Mul M₀'] →
        [inst_2 : SemigroupWithZero M₀] →
          (f : M₀' → M₀) →
            Function.Injective f → f 0 = 0 → (∀ (x y : M₀'), f (x * y) = f x * f y) → SemigroupWithZero M₀'

Pull back a SemigroupWithZero along an injective function. See note [reducible non-instances].

Defined in

Mathlib.Algebra.GroupWithZero.InjSurj

Cited by

0 results in Mathlib

Foundations

Depth 9 from the axioms · uses propext

Assumes

ZeroMulSemigroupWithZero