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Theorems · Theorem · ring theory

NonUnitalSubsemiring.gc_map_comap

∀ {R : Type u} {S : Type v} [inst : NonUnitalNonAssocSemiring R] [inst_1 : NonUnitalNonAssocSemiring S] {F : Type u_1}
  [inst_2 : FunLike F R S] [inst_3 : NonUnitalRingHomClass F R S] (f : F),
  GaloisConnection (NonUnitalSubsemiring.map f) (NonUnitalSubsemiring.comap f)
Defined in
Mathlib.RingTheory.NonUnitalSubsemiring.Basic
Cited by
7 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Quot.sound
Assumes
NonUnitalNonAssocSemiringNonUnitalNonAssocSemiringFunLikeNonUnitalRingHomClass
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Around this declaration

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

NonUnitalSubsemiring.comap_top · cited by 1NonUnitalSubsemiring.coma…NonUnitalSubsemiring.comap_inf · cited by 0NonUnitalSubsemiring.coma…NonUnitalSubsemiring.map_bot · cited by 0NonUnitalSubsemiring.map_…NonUnitalSubsemiring.map_iSup · cited by 0NonUnitalSubsemiring.map_…NonUnitalRingHom.map_sclosure · cited by 0NonUnitalRingHom.map_sclo…NonUnitalSubsemiring.map_sup · cited by 0NonUnitalSubsemiring.map_…NonUnitalSubsemiring.comap_iInf · cited by 0NonUnitalSubsemiring.coma…FunLike · cited by 2560FunLikeNonUnitalNonAssocSemiring · cited by 1081NonUnitalNonAssocSemiringGaloisConnection · cited by 253GaloisConnectionNonUnitalSubsemiring · cited by 201NonUnitalSubsemiringNonUnitalRingHomClass · cited by 82NonUnitalRingHomClassNonUnitalSubsemiring.map · cited by 22NonUnitalSubsemiring.mapNonUnitalSubsemiring.comap · cited by 14NonUnitalSubsemiring.comapNonUnitalSubsemiring.map_le_iff_le_comap · cited by 1NonUnitalSubsemiring.map_…NonUnitalSubsemiring.gc_map_c…CITED BYCITES

Cites8

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Cited by7

Results whose statement or proof uses this declaration.