Theorems · Definition · commutative algebra
RingHom.StableUnderComposition
({R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop) → PropA property is StableUnderComposition if the composition of two such morphisms
still falls in the class.
- Defined in
- Mathlib.RingTheory.RingHomProperties
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.compproof · cited by 899
Cited by26
Results whose statement or proof uses this declaration.
- RingHom.StableUnderComposition.respectsIsostatement and proof · cited by 15
- RingHom.StableUnderComposition.stableUnderCompositionWithLocalizationAwaystatement and proof · cited by 7
- RingHom.FormallyUnramified.stableUnderCompositionstatement · cited by 4
- RingHom.HoldsForLocalization.localRingHomstatement and proof · cited by 2
- RingHom.EssFiniteType.stableUnderCompositionstatement · cited by 2
- RingHom.finitePresentation_stableUnderCompositionstatement · cited by 2
- RingHom.Flat.stableUnderCompositionstatement · cited by 2
- RingHom.finiteType_stableUnderCompositionstatement · cited by 2
- RingHom.QuasiFinite.stableUnderCompositionstatement · cited by 2
- RingHom.isStandardSmooth_stableUnderCompositionstatement · cited by 2
- RingHom.Smooth.stableUnderCompositionstatement · cited by 2
- RingHom.surjective_stableUnderCompositionstatement · cited by 1