Theorems · Definition · category theory
CategoryTheory.Limits.WidePullbackShape.wideCospan
{J : Type w} →
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
(B : C) →
(objs : J → C) → ((j : J) → objs j ⟶ B) → CategoryTheory.Functor (CategoryTheory.Limits.WidePullbackShape J) CConstruct a functor out of the wide pullback shape given a J-indexed collection of arrows to a fixed object.
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses no axioms
- 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.Functorstatement · cited by 16,252
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Limits.WidePullbackShapestatement and proof · cited by 94
- CategoryTheory.Limits.WidePullbackShape.Hom.casesOnproof · cited by 1
Cited by42
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.cospanproof · cited by 467
- CategoryTheory.Limits.HasWidePullbackproof · cited by 44
- CategoryTheory.Limits.widePullbackproof · cited by 31
- CategoryTheory.Limits.WidePullback.πproof · cited by 28
- CategoryTheory.Limits.WidePullback.baseproof · cited by 20
- CategoryTheory.Over.ConstructProducts.widePullbackDiagramOfDiagramOverproof · cited by 16
- CategoryTheory.Limits.WidePullback.liftproof · cited by 12
- CategoryTheory.Limits.WidePullbackConeproof · cited by 11
- CategoryTheory.Limits.WidePullbackCone.basestatement · cited by 7
- CategoryTheory.Limits.WidePullbackCone.πstatement · cited by 7
- CategoryTheory.Limits.FormalCoproduct.cechIsoCechNerveAppproof · cited by 6
- CategoryTheory.Limits.WidePullbackCone.IsLimit.liftstatement · cited by 5