Theorems · Definition · commutative algebra
CommRingCat.regularMonoOfFaithfullyFlat
{R S : CommRingCat} → (f : R ⟶ S) → (CommRingCat.Hom.hom f).FaithfullyFlat → CategoryTheory.RegularMono fA regular monomorphism structure on a map f : R ⟶ S in CommRingCat with
faithfully flat f.hom : R ⟶ S.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CommRingCatstatement and proof · cited by 2,333
- CommRingCat.carrierstatement · cited by 1,096
- CommRingCat.Hom.homstatement and proof · cited by 432
- CategoryTheory.Limits.pushoutproof · cited by 284
- CategoryTheory.Limits.pushout.inrproof · cited by 193
- CategoryTheory.Limits.pushout.inlproof · cited by 192
- RingHom.FaithfullyFlatstatement and proof · cited by 25
- CategoryTheory.RegularMonostatement · cited by 14
- CommRingCat.isLimitForkPushoutSelfOfFaithfullyFlatproof · cited by 0
Cited by1
Results whose statement or proof uses this declaration.
- CommRingCat.isRegularMono_of_faithfullyFlatproof · cited by 1