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Theorems · Definition · group theory

Function.Injective.mulZeroClass

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

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

Defined in
Mathlib.Algebra.GroupWithZero.InjSurj
Cited by
0 results in Mathlib
Foundations
Depth 7 from the axioms · uses propext
Assumes
MulZeroClassMulZero
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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Function.Injective.commMonoidWithZero · cited by 0Injective.commMonoidWithZ…Equiv.mulZeroClass · cited by 0Equiv.mulZeroClassFunction.Injective.mulZeroOneClass · cited by 0Injective.mulZeroOneClassFunction.Injective.nonUnitalNonAssocSemiring · cited by 0Injective.nonUnitalNonAss…Function.Injective.monoidWithZero · cited by 0Injective.monoidWithZeroFunction.Injective.semigroupWithZero · cited by 0Injective.semigroupWithZe…MulZeroClass · cited by 232MulZeroClassInjective.mulZeroClassCITED BYCITES

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