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Theorems · Definition · group theory

AddHom.subsemigroupMap

{M : Type u_1} →
  {N : Type u_2} →
    [inst : Add M] → [inst_1 : Add N] → (f : M →ₙ+ N) → (M' : AddSubsemigroup M) → ↥M' →ₙ+ ↥(AddSubsemigroup.map f M')

the AddHom from an additive subsemigroup to its image. See AddEquiv.addSubsemigroupMap for a variant for AddEquivs.

Defined in
Mathlib.Algebra.Group.Subsemigroup.Operations
Cited by
2 results in Mathlib
Foundations
Depth 13 from the axioms · uses no axioms
Assumes
AddAdd
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AddEquiv.subsemigroupMap · cited by 2AddEquiv.subsemigroupMapAddHom.subsemigroupMap_apply_coe · cited by 0AddHom.subsemigroupMap_ap…AddHom.subsemigroupMap_surjective · cited by 0AddHom.subsemigroupMap_su…DFunLike.coe · cited by 62936DFunLike.coeAddHom · cited by 294AddHomAddSubsemigroup · cited by 262AddSubsemigroupAddSubsemigroup.map · cited by 50AddSubsemigroup.mapAddHom.subsemigroupMapCITED BYCITES

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