Theorems · Theorem · category theory
CategoryTheory.IsPullback.flip
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P X Y Z : C} {fst : P ⟶ X} {snd : P ⟶ Y} {f : X ⟶ Z}
{g : Y ⟶ Z}, CategoryTheory.IsPullback fst snd f g → CategoryTheory.IsPullback snd fst g f- Cited by
- 61 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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 and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.IsPullbackstatement and proof · cited by 320
- CategoryTheory.IsPullback.isLimitproof · cited by 47
- CategoryTheory.IsPullback.of_isLimitproof · cited by 12
- CategoryTheory.Limits.PullbackCone.flipIsLimitproof · cited by 6
Cited by61
Results whose statement or proof uses this declaration.
- CategoryTheory.IsPullback.of_rightproof · cited by 14
- CategoryTheory.IsPullback.paste_horizproof · cited by 14
- AlgebraicGeometry.IsZariskiLocalAtTarget.restrictproof · cited by 8
- CategoryTheory.IsPullback.unopproof · cited by 6
- AlgebraicGeometry.Scheme.Hom.support_kerproof · cited by 6
- CategoryTheory.IsPullback.opproof · cited by 5
- CategoryTheory.MorphismProperty.pullback_fstproof · cited by 4
- CategoryTheory.MorphismProperty.universally_eq_iffproof · cited by 3
- AlgebraicGeometry.AffineSpace.isPullback_mapproof · cited by 2
- CategoryTheory.isUniversalColimit_extendCofanproof · cited by 2
- AlgebraicGeometry.IsIntegralHom.iff_universallyClosed_and_isAffineHomproof · cited by 2