Theorems · Definition · commutative algebra
RingHom.HasStableEqualizers
({R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop) → PropA property P of ring homomorphisms is said to have stable equalizers, if the equalizer
of algebra maps between algebras with structure morphisms satisfying P, is preserved by
arbitrary base change.
- Defined in
- Mathlib.RingTheory.Flat.Equalizer
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebraproof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- Algebra.algebraMapproof · cited by 4,706
- AlgHomproof · cited by 3,236
- Function.Bijectiveproof · cited by 863
- AlgHom.tensorEqualizerproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- RingHom.HasStableEqualizers.preservesLimit_parallelPair_tensorProdstatement and proof · cited by 1
- RingHom.HasStableEqualizers.preservesEqualizers_pushoutstatement and proof · cited by 1
- RingHom.HasStableEqualizers.preservesFiniteLimits_pushoutstatement and proof · cited by 0