Theorems · Theorem · commutative algebra
RingHom.PropertyIsLocal.respectsIso
∀ {P : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop},
RingHom.PropertyIsLocal P → RingHom.RespectsIso P- Defined in
- Mathlib.RingTheory.LocalProperties.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- RingHom.RespectsIsostatement · cited by 78
- RingHom.PropertyIsLocalstatement and proof · cited by 20
- RingHom.LocalizationAwayPreserves.respectsIsoproof · cited by 4
- RingHom.PropertyIsLocal.localizationAwayPreservesproof · cited by 4
Cited by16
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.HasRingHomProperty.Spec_iffproof · cited by 19
- AlgebraicGeometry.HasRingHomProperty.comp_of_isOpenImmersionproof · cited by 4
- AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE_locallyproof · cited by 3
- AlgebraicGeometry.HasRingHomProperty.stalkMapproof · cited by 3
- RingHom.Etale.respectsIsoproof · cited by 2
- AlgebraicGeometry.HasRingHomProperty.of_source_openCoverproof · cited by 2
- AlgebraicGeometry.exists_smooth_of_formallySmooth_stalkproof · cited by 2
- AlgebraicGeometry.HasRingHomProperty.isStableUnderBaseChangeproof · cited by 1
- AlgebraicGeometry.HasRingHomProperty.of_stalkMapproof · cited by 1
- RingHom.smooth_iff_locally_isStandardSmoothproof · cited by 1
- AlgebraicGeometry.targetAffineLocally_affineAnd_iff_affineLocallyproof · cited by 1
- RingHom.Smooth.respectsIsoproof · cited by 1