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Theorems · Theorem · group theory

AddSubsemigroup.gc_map_comap

∀ {M : Type u_1} {N : Type u_2} [inst : Add M] [inst_1 : Add N] (f : M →ₙ+ N),
  GaloisConnection (AddSubsemigroup.map f) (AddSubsemigroup.comap f)
Defined in
Mathlib.Algebra.Group.Subsemigroup.Operations
Cited by
15 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Quot.sound
Assumes
AddAdd
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Around this declaration

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

AddSubsemigroup.gciMapComap · cited by 9AddSubsemigroup.gciMapCom…AddSubsemigroup.giMapComap · cited by 9AddSubsemigroup.giMapComapAddSubsemigroup.comap_top · cited by 1AddSubsemigroup.comap_topAddHom.map_mclosure · cited by 0AddHom.map_mclosureAddSubsemigroup.monotone_comap · cited by 0AddSubsemigroup.monotone_…AddSubsemigroup.le_comap_map · cited by 0AddSubsemigroup.le_comap_…AddSubsemigroup.le_comap_of_map_le · cited by 0AddSubsemigroup.le_comap_…AddSubsemigroup.monotone_map · cited by 0AddSubsemigroup.monotone_…AddSubsemigroup.map_bot · cited by 0AddSubsemigroup.map_botAddSubsemigroup.map_comap_le · cited by 0AddSubsemigroup.map_comap…AddSubsemigroup.comap_iInf · cited by 0AddSubsemigroup.comap_iInfAddSubsemigroup.map_comap_map · cited by 0AddSubsemigroup.map_comap…AddSubsemigroup.comap_inf · cited by 0AddSubsemigroup.comap_infAddSubsemigroup.map_iSup · cited by 0AddSubsemigroup.map_iSupAddSubsemigroup.comap_map_comap · cited by 0AddSubsemigroup.comap_map…AddHom · cited by 294AddHomAddSubsemigroup · cited by 262AddSubsemigroupGaloisConnection · cited by 253GaloisConnectionAddSubsemigroup.map · cited by 50AddSubsemigroup.mapAddSubsemigroup.comap · cited by 39AddSubsemigroup.comapAddSubsemigroup.map_le_iff_le_comap · cited by 1AddSubsemigroup.map_le_if…AddSubsemigroup.gc_map_comapCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by17

Results whose statement or proof uses this declaration.