Theorems · Definition · category theory
CategoryTheory.Limits.HasPullback
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → {X Y Z : C} → (X ⟶ Z) → (Y ⟶ Z) → PropTwo morphisms f : X ⟶ Z and g : Y ⟶ Z have a pullback if the diagram cospan f g has a
limit.
- Cited by
- 434 results in Mathlib
- Foundations
- Depth 17 from the axioms, rests on 87 definitions · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.cospanproof · cited by 467
- CategoryTheory.Limits.HasLimitproof · cited by 226
Cited by556
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.pullbackstatement and proof · cited by 864
- CategoryTheory.Limits.pullback.fststatement and proof · cited by 639
- CategoryTheory.Limits.pullback.sndstatement and proof · cited by 637
- CategoryTheory.Limits.pullback.mapstatement and proof · cited by 156
- CategoryTheory.Limits.pullback.conditionstatement and proof · cited by 122
- CategoryTheory.Limits.pullback.liftstatement and proof · cited by 114
- CategoryTheory.Limits.pullback.diagonalObjstatement and proof · cited by 80
- CategoryTheory.IsPullback.of_hasPullbackstatement and proof · cited by 70
- CategoryTheory.Limits.pullback.diagonalstatement and proof · cited by 67
- CategoryTheory.Precoverage.ZeroHypercover.pullback₁statement and proof · cited by 64
- CategoryTheory.Limits.pullback.hom_extstatement and proof · cited by 63
- CategoryTheory.Limits.pullbackSymmetrystatement and proof · cited by 61
Showing the 200 most cited of 556.