Theorems · Theorem · category theory
CommRingCat.Under.preservesFiniteLimits_of_flat
∀ {R S : CommRingCat} (f : R ⟶ S),
(CommRingCat.Hom.hom f).Flat → CategoryTheory.Limits.PreservesFiniteLimits (CategoryTheory.Under.pushout f)Under.pushout f preserves finite limits if f is flat.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
- CommRingCat.carrierstatement · cited by 1,096
- CategoryTheory.SmallCategoryproof · cited by 480
- CommRingCat.Hom.homstatement and proof · cited by 432
- CategoryTheory.Limits.WalkingSpanstatement · cited by 300
- CategoryTheory.Limits.spanstatement · cited by 294
- CategoryTheory.Understatement · cited by 276
- CategoryTheory.Limits.PreservesFiniteLimitsstatement · cited by 121
- CategoryTheory.FinCategoryproof · cited by 107
- RingHom.Flatstatement and proof · cited by 60
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isIso_pushoutSection_of_iSup_eqproof · cited by 2