Theorems · Definition · group theory

Function.Injective.monoidWithZero

{M₀ : Type u_1} →
  {M₀' : Type u_3} →
    [inst : Zero M₀'] →
      [inst_1 : Mul M₀'] →
        [inst_2 : One M₀'] →
          [inst_3 : Pow M₀' ℕ] →
            [inst_4 : MonoidWithZero M₀] →
              (f : M₀' → M₀) →
                Function.Injective f →
                  f 0 = 0 →
                    f 1 = 1 →
                      (∀ (x y : M₀'), f (x * y) = f x * f y) →
                        (∀ (x : M₀') (n : ℕ), f (x ^ n) = f x ^ n) → MonoidWithZero M₀'

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

Defined in

Mathlib.Algebra.GroupWithZero.InjSurj

Cited by

0 results in Mathlib

Foundations

Depth 13 from the axioms · uses propext

Assumes

ZeroMulOnePowMonoidWithZero