Theorems · Definition · category theory
CategoryTheory.Limits.HasWidePullback
{J : Type w} →
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → (B : C) → (objs : J → C) → ((j : J) → objs j ⟶ B) → PropHasWidePullback B objs arrows means that wideCospan B objs arrows has a limit.
- Cited by
- 44 results in Mathlib
- Foundations
- Depth 16 from the axioms · 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.HasLimitproof · cited by 226
- CategoryTheory.Limits.WidePullbackShape.wideCospanproof · cited by 22
Cited by60
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.widePullbackstatement and proof · cited by 31
- CategoryTheory.Limits.WidePullback.πstatement and proof · cited by 28
- CategoryTheory.Limits.WidePullback.basestatement and proof · cited by 20
- CategoryTheory.Arrow.cechNervestatement and proof · cited by 18
- CategoryTheory.Arrow.augmentedCechNervestatement and proof · cited by 16
- CategoryTheory.Limits.WidePullback.liftstatement and proof · cited by 12
- CategoryTheory.SimplicialObject.augmentedCechNervestatement and proof · cited by 7
- CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.sstatement and proof · cited by 6
- CategoryTheory.SimplicialObject.equivalenceLeftToRightstatement and proof · cited by 3
- CategoryTheory.SimplicialObject.equivalenceRightToLeftstatement and proof · cited by 3
- CategoryTheory.Arrow.mapCechNervestatement and proof · cited by 3
- CategoryTheory.SimplicialObject.cechNervestatement and proof · cited by 2