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Theorems · Definition · group theory

AddSubsemigroup.comap

{M : Type u_1} → {N : Type u_2} → [inst : Add M] → [inst_1 : Add N] → (M →ₙ+ N) → AddSubsemigroup N → AddSubsemigroup M

The preimage of an AddSubsemigroup along an AddSemigroup homomorphism is an AddSubsemigroup.

Defined in
Mathlib.Algebra.Group.Subsemigroup.Operations
Cited by
39 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Assumes
AddAdd
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Around this declaration

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

AddSubsemigroup.gc_map_comap · cited by 15AddSubsemigroup.gc_map_co…AddSubsemigroup.gciMapComap · cited by 9AddSubsemigroup.gciMapCom…AddSubsemigroup.giMapComap · cited by 9AddSubsemigroup.giMapComapAddSubsemigroup.mem_comap · cited by 4AddSubsemigroup.mem_comapAddHom.subsemigroupComap · cited by 1AddHom.subsemigroupComapAddSubsemigroup.top_prod · cited by 1AddSubsemigroup.top_prodAddSubsemigroup.map_comap_eq · cited by 1AddSubsemigroup.map_comap…AddSubsemigroup.map_equiv_eq_comap_symm · cited by 1AddSubsemigroup.map_equiv…AddSubsemigroup.map_le_iff_le_comap · cited by 1AddSubsemigroup.map_le_if…AddSubsemigroup.comap_top · cited by 1AddSubsemigroup.comap_topAddSubsemigroup.prod_top · cited by 0AddSubsemigroup.prod_topAddHom.subsemigroupComap_apply_coe · cited by 0AddHom.subsemigroupComap_…AddSubsemigroup.le_comap_map · cited by 0AddSubsemigroup.le_comap_…AddSubsemigroup.le_comap_of_map_le · cited by 0AddSubsemigroup.le_comap_…AddSubsemigroup.map_comap_eq_of_surjective · cited by 0AddSubsemigroup.map_comap…DFunLike.coe · cited by 62936DFunLike.coeSetLike.coe · cited by 8199SetLike.coeSet.preimage · cited by 4946Set.preimageAddHom · cited by 294AddHomAddSubsemigroup · cited by 262AddSubsemigroupAddSubsemigroup.comapCITED BYCITES

Cites5

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Cited by42

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