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Theorems · Definition · group theory

Function.Surjective.mulZeroClass

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

Push forward a MulZeroClass instance along a surjective 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
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Around this declaration

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Function.Surjective.mulZeroOneClass · cited by 0Surjective.mulZeroOneClassFunction.Surjective.semigroupWithZero · cited by 0Surjective.semigroupWithZ…Function.Surjective.commMonoidWithZero · cited by 0Surjective.commMonoidWith…Function.Surjective.nonUnitalNonAssocSemiring · cited by 0Surjective.nonUnitalNonAs…Function.Surjective.monoidWithZero · cited by 0Surjective.monoidWithZeroMulZeroClass · cited by 232MulZeroClassSurjective.mulZeroClassCITED BYCITES

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