Theorems · Theorem · category theory
CategoryTheory.IsPullback.hasPullback
∀ {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.Limits.HasPullback f g- Cited by
- 8 results in Mathlib
- Foundations
- Depth 27 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.Limits.HasPullbackstatement · cited by 434
- CategoryTheory.IsPullbackstatement and proof · cited by 320
- CategoryTheory.IsPullback.isLimitproof · cited by 47
- CategoryTheory.IsPullback.coneproof · cited by 16
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.IsStableUnderBaseChange.mk'proof · cited by 2
- CategoryTheory.MorphismProperty.IsLocalAtTarget.of_isPullbackproof · cited by 1
- CategoryTheory.MorphismProperty.universally_mk'proof · cited by 1
- CategoryTheory.IsPullback.isIso_fst_of_isIsoproof · cited by 1
- CategoryTheory.MorphismProperty.DescendsAlong.mk'proof · cited by 1
- CategoryTheory.IsPushout.isVanKampen_iff'proof · cited by 0