Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.of_isPullback
∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {P : CategoryTheory.MorphismProperty C}
[self : P.IsStableUnderBaseChange] {X Y Y' S : C} {f : X ⟶ S} {g : Y ⟶ S} {f' : Y' ⟶ Y} {g' : Y' ⟶ X},
CategoryTheory.IsPullback f' g' g f → P g → P g'Alias of CategoryTheory.MorphismProperty.IsStableUnderBaseChange.of_isPullback.
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.MorphismPropertystatement · cited by 2,179
- CategoryTheory.IsPullbackstatement · cited by 320
- CategoryTheory.MorphismProperty.IsStableUnderBaseChangestatement · cited by 131
- CategoryTheory.MorphismProperty.IsStableUnderBaseChange.of_isPullbackproof · cited by 3
Cited by14
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.iff_of_isPullbackproof · cited by 2
- AlgebraicGeometry.Scheme.ker_ideal_of_isPullback_of_isOpenImmersionproof · cited by 2
- CategoryTheory.MorphismProperty.pullbackLift_fst_sndproof · cited by 2
- CategoryTheory.MorphismProperty.isStableUnderBaseChange_iff_pullbacks_leproof · cited by 1
- CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.isIso_fproof · cited by 1
- CategoryTheory.Square.IsPullback.mono_f₁₃proof · cited by 1
- AlgebraicGeometry.universally_isZariskiLocalAtTargetproof · cited by 0
- AlgebraicGeometry.Scheme.Hom.isConstructible_preimageproof · cited by 0
- CategoryTheory.CostructuredArrow.closedUnderLimitsOfShape_walkingCospanproof · cited by 0
- CategoryTheory.MorphismProperty.hasOfPostcompProperty_iff_le_diagonalproof · cited by 0
- AlgebraicGeometry.Smooth.of_smooth_fiberToSpecResidueFieldproof · cited by 0
- HomotopicalAlgebra.ModelCategory.hasLiftingProperty_of_joyalTrickDualproof · cited by 0