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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.

AlgebraicGeometry.HasRingHomProperty.Spec_iff · cited by 19HasRingHomProperty.Spec_i…AlgebraicGeometry.HasRingHomProperty.comp_of_isOpenImmersion · cited by 4HasRingHomProperty.comp_o…AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE_locally · cited by 3HasRingHomProperty.iff_ex…AlgebraicGeometry.HasRingHomProperty.stalkMap · cited by 3HasRingHomProperty.stalkM…RingHom.Etale.respectsIso · cited by 2Etale.respectsIsoAlgebraicGeometry.HasRingHomProperty.of_source_openCover · cited by 2HasRingHomProperty.of_sou…AlgebraicGeometry.exists_smooth_of_formallySmooth_stalk · cited by 2AlgebraicGeometry.exists_…AlgebraicGeometry.HasRingHomProperty.isStableUnderBaseChange · cited by 1HasRingHomProperty.isStab…AlgebraicGeometry.HasRingHomProperty.of_stalkMap · cited by 1HasRingHomProperty.of_sta…RingHom.smooth_iff_locally_isStandardSmooth · cited by 1RingHom.smooth_iff_locall…AlgebraicGeometry.targetAffineLocally_affineAnd_iff_affineLocally · cited by 1AlgebraicGeometry.targetA…RingHom.Smooth.respectsIso · cited by 1Smooth.respectsIsoAlgebraicGeometry.HasRingHomProperty.iff_exists_appLE · cited by 0HasRingHomProperty.iff_ex…AlgebraicGeometry.Scheme.Hom.smoothLocus_eq_top_iff · cited by 0Hom.smoothLocus_eq_top_iffAlgebraicGeometry.affineAnd_isLocal_of_propertyIsLocal · cited by 0AlgebraicGeometry.affineA…CommRing · cited by 17173CommRingRingHom · cited by 10189RingHomRingHom.RespectsIso · cited by 78RingHom.RespectsIsoRingHom.PropertyIsLocal · cited by 20RingHom.PropertyIsLocalRingHom.LocalizationAwayPreserves.respectsIso · cited by 4LocalizationAwayPreserves…RingHom.PropertyIsLocal.localizationAwayPreserves · cited by 4PropertyIsLocal.localizat…PropertyIsLocal.respectsIsoCITED BYCITES

Cites6

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

Cited by16

Results whose statement or proof uses this declaration.