Theorems · Definition · category theory
CategoryTheory.Limits.pullback.isLimit
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{X Y Z : C} →
(f : X ⟶ Z) →
(g : Y ⟶ Z) →
[inst_1 : CategoryTheory.Limits.HasPullback f g] →
CategoryTheory.Limits.IsLimit (CategoryTheory.Limits.pullback.cone f g)The cone associated to a pullback is a limit cone.
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.WalkingPairstatement · cited by 1,319
- CategoryTheory.Limits.IsLimitstatement · cited by 664
- CategoryTheory.Limits.WalkingCospanstatement · cited by 496
- CategoryTheory.Limits.cospanstatement and proof · cited by 467
- CategoryTheory.Limits.HasPullbackstatement and proof · cited by 434
- CategoryTheory.Limits.limit.isLimitproof · cited by 146
- CategoryTheory.Limits.pullback.conestatement · cited by 18
Cited by33
Results whose statement or proof uses this declaration.
- CategoryTheory.Over.cartesianMonoidalCategoryproof · cited by 68
- CategoryTheory.Limits.pullbackRightPullbackFstIsoproof · cited by 43
- CategoryTheory.Limits.pullbackLeftPullbackSndIsoproof · cited by 19
- CategoryTheory.Limits.pullbackIsPullbackproof · cited by 14
- CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_snd_sndproof · cited by 8
- CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_sndproof · cited by 7
- CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_fstproof · cited by 5
- CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_fstproof · cited by 4
- CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_fstproof · cited by 3
- CategoryTheory.Limits.pullbackLeftPullbackSndIso_hom_fstproof · cited by 3
- CategoryTheory.Limits.pullbackLeftPullbackSndIso_inv_snd_sndproof · cited by 2
- CategoryTheory.Limits.IsInitial.ofCoproductDisjointOfIsColimitproof · cited by 2