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Theorems · Theorem · commutative algebra

RingHom.toMorphismProperty_respectsIso_iff

∀ {P : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop},
  (RingHom.RespectsIso fun {R S} [CommRing R] [CommRing S] => P) ↔
    (RingHom.toMorphismProperty fun {R S} [CommRing R] [CommRing S] => P).RespectsIso
Defined in
Mathlib.RingTheory.RingHomProperties
Cited by
11 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

RingHom.RespectsIso.arrow_mk_iso_iff · cited by 6RespectsIso.arrow_mk_iso_…AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE_locally · cited by 3HasRingHomProperty.iff_ex…AlgebraicGeometry.IsIntegralHom.SpecMap_iff · cited by 2IsIntegralHom.SpecMap_iffAlgebraicGeometry.stalkwise_SpecMap_iff · cited by 2AlgebraicGeometry.stalkwi…AlgebraicGeometry.IsSeparated.valuativeCriterion · cited by 1IsSeparated.valuativeCrit…AlgebraicGeometry.HasRingHomProperty.isLocal_ringHomProperty_of_isZariskiLocalAtSource_of_isZariskiLocalAtTarget · cited by 1HasRingHomProperty.isLoca…AlgebraicGeometry.HasAffineProperty.SpecMap_iff_of_affineAnd · cited by 1HasAffineProperty.SpecMap…AlgebraicGeometry.stalkwiseIsZariskiLocalAtTarget_of_respectsIso · cited by 1AlgebraicGeometry.stalkwi…RingHom.HasFiniteProducts.isClosedUnderLimitsOfShape · cited by 0HasFiniteProducts.isClose…AlgebraicGeometry.AffineSpace.isIntegralHom_over_iff_isEmpty · cited by 0AffineSpace.isIntegralHom…RingHom.HasEqualizers.isClosedUnderLimitsOfShape · cited by 0HasEqualizers.isClosedUnd…Quiver.Hom · cited by 32603Quiver.HomCommRing · cited by 17173CommRingRingHom · cited by 10189RingHomCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCommRingCat · cited by 2333CommRingCatRingEquiv · cited by 1147RingEquivCommRingCat.carrier · cited by 1096CommRingCat.carrierCommRingCat.Hom.hom · cited by 432Hom.homCommRingCat.ofHom · cited by 259CommRingCat.ofHomCategoryTheory.MorphismProperty.RespectsIso · cited by 248MorphismProperty.Respects…RingHom.RespectsIso · cited by 78RingHom.RespectsIsoCategoryTheory.Iso.commRingCatIsoToRingEquiv · cited by 44Iso.commRingCatIsoToRingE…RingEquiv.toCommRingCatIso · cited by 19RingEquiv.toCommRingCatIsoRingHom.toMorphismProperty · cited by 19RingHom.toMorphismPropertyRingHom.toMorphismProperty_re…CITED BYCITES

Cites18

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

Cited by11

Results whose statement or proof uses this declaration.