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Theorems · Theorem · group theory

MulEquiv.map_one

∀ {M : Type u_4} {N : Type u_5} [inst : MulOneClass M] [inst_1 : MulOneClass N] (h : M ≃* N), h 1 = 1

A multiplicative isomorphism of monoids sends 1 to 1 (and is hence a monoid isomorphism).

Defined in
Mathlib.Algebra.Group.Equiv.Defs
Cited by
2 results in Mathlib
Foundations
Depth 18 from the axioms · uses Quot.sound
Assumes
MulOneClassMulOneClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MulEquiv.toMonoidHom · cited by 126MulEquiv.toMonoidHomstar_one · cited by 33star_oneSubmonoid.isLocalizationMap_iff_bijective · cited by 1Submonoid.isLocalizationM…DFunLike.coe · cited by 62936DFunLike.coeMulEquiv · cited by 1142MulEquivMulOneClass · cited by 1018MulOneClassmap_one · cited by 861map_oneMulEquiv.map_oneCITED BYCITES

Cites4

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Cited by3

Results whose statement or proof uses this declaration.