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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.Isoproof · cited by 3,963
- CommRingCatstatement and proof · cited by 2,333
- RingEquivproof · cited by 1,147
- CommRingCat.carrierproof · cited by 1,096
- CommRingCat.Hom.homproof · cited by 432
- CommRingCat.ofHomproof · cited by 259
- CategoryTheory.MorphismProperty.RespectsIsostatement and proof · cited by 248
- RingHom.RespectsIsostatement and proof · cited by 78
Cited by11
Results whose statement or proof uses this declaration.
- RingHom.RespectsIso.arrow_mk_iso_iffproof · cited by 6
- AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE_locallyproof · cited by 3
- AlgebraicGeometry.IsIntegralHom.SpecMap_iffproof · cited by 2
- AlgebraicGeometry.stalkwise_SpecMap_iffproof · cited by 2
- AlgebraicGeometry.IsSeparated.valuativeCriterionproof · cited by 1
- AlgebraicGeometry.HasAffineProperty.SpecMap_iff_of_affineAndproof · cited by 1
- AlgebraicGeometry.stalkwiseIsZariskiLocalAtTarget_of_respectsIsoproof · cited by 1
- RingHom.HasFiniteProducts.isClosedUnderLimitsOfShapeproof · cited by 0
- AlgebraicGeometry.AffineSpace.isIntegralHom_over_iff_isEmptyproof · cited by 0
- RingHom.HasEqualizers.isClosedUnderLimitsOfShapeproof · cited by 0