Theorems · Definition · commutative algebra
CommRingCat.isLimitForkPushoutSelfOfFaithfullyFlat
{R S : CommRingCat} →
(f : R ⟶ S) →
(CommRingCat.Hom.hom f).FaithfullyFlat → CategoryTheory.Limits.IsLimit (CategoryTheory.Limits.Fork.ofι f ⋯)If f : R ⟶ S is a faithfully flat map in CommRingCat, then the fork
``
S inl > pushout f f
R --f-->
S inr > pushout f f
``
is an equalizer diagram.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Quiver.Homstatement and proof · cited by 32,603
- Algebraproof · cited by 11,388
- Algebra.algebraMapproof · cited by 4,706
- Equiv.symmproof · cited by 3,681
- CommRingCatstatement and proof · cited by 2,333
- CategoryTheory.Limits.Cocone.ptproof · cited by 1,354
- CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
- CategoryTheory.Limits.Cone.ptproof · cited by 1,298
- CommRingCat.carrierstatement and proof · cited by 1,096
- CategoryTheory.Limits.WalkingParallelPairstatement · cited by 781
- CategoryTheory.Limits.parallelPairstatement · cited by 766
Cited by1
Results whose statement or proof uses this declaration.
- CommRingCat.regularMonoOfFaithfullyFlatproof · cited by 1