Theorems · Definition · category theory
CategoryTheory.Limits.pullback
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{X Y Z : C} → (f : X ⟶ Z) → (g : Y ⟶ Z) → [CategoryTheory.Limits.HasPullback f g] → Cpullback f g computes the pullback of a pair of morphisms with the same target.
- Cited by
- 864 results in Mathlib
- Foundations
- Depth 18 from the axioms, rests on 96 definitions · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.HasPullbackstatement and proof · cited by 434
- CategoryTheory.Limits.limitproof · cited by 346
Cited by1,026
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.pullback.fststatement · cited by 639
- CategoryTheory.Limits.pullback.sndstatement · cited by 637
- CategoryTheory.Limits.pullback.mapstatement · cited by 156
- CategoryTheory.Limits.pullback.conditionstatement · cited by 122
- CategoryTheory.Limits.pullback.liftstatement · cited by 114
- CategoryTheory.Limits.pullback.diagonalObjproof · cited by 80
- CategoryTheory.IsPullback.of_hasPullbackstatement · cited by 70
- CategoryTheory.Limits.pullback.hom_extstatement and proof · cited by 63
- CategoryTheory.Limits.pullbackSymmetrystatement · cited by 61
- AlgebraicGeometry.AffineSpaceproof · cited by 51
- CategoryTheory.Limits.pullbackRightPullbackFstIsostatement · cited by 43
- CategoryTheory.IsPullback.isoPullbackstatement · cited by 42
Showing the 200 most cited of 1,026.