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Theorems · Theorem · group theory

MonoidHom.map_exists_left_inv

∀ {M : Type u_4} {N : Type u_5} {F : Type u_9} [inst : MulOne M] [inst_1 : MulOne N] [inst_2 : FunLike F M N]
  [MonoidHomClass F M N] (f : F) {x : M}, (∃ y, y * x = 1) → ∃ y, y * f x = 1

Given a monoid homomorphism f : M →* N and an element x : M, if x has a left inverse, then f x has a left inverse too. For elements invertible on both sides see IsUnit.map.

Defined in
Mathlib.Algebra.Group.Hom.Defs
Cited by
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Foundations
Depth 7 from the axioms · uses no axioms
Assumes
MulOneMulOneFunLikeMonoidHomClass
Mathlib docsSourceLoogleLeanSearch

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DFunLike.coe · cited by 62936DFunLike.coeFunLike · cited by 2560FunLikeMonoidHomClass · cited by 244MonoidHomClassMulOne · cited by 65MulOnemap_mul_eq_one · cited by 6map_mul_eq_oneMonoidHom.map_exists_left_invCITED BYCITES

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