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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) C

Construct a functor out of the wide pullback shape given a J-indexed collection of arrows to a fixed object.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks
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.

CategoryTheory.Limits.cospan · cited by 467Limits.cospanCategoryTheory.Limits.HasWidePullback · cited by 44Limits.HasWidePullbackCategoryTheory.Limits.widePullback · cited by 31Limits.widePullbackCategoryTheory.Limits.WidePullback.π · cited by 28WidePullback.πCategoryTheory.Limits.WidePullback.base · cited by 20WidePullback.baseCategoryTheory.Over.ConstructProducts.widePullbackDiagramOfDiagramOver · cited by 16ConstructProducts.widePul…CategoryTheory.Limits.WidePullback.lift · cited by 12WidePullback.liftCategoryTheory.Limits.WidePullbackCone · cited by 11Limits.WidePullbackConeCategoryTheory.Limits.WidePullbackCone.base · cited by 7WidePullbackCone.baseCategoryTheory.Limits.WidePullbackCone.π · cited by 7WidePullbackCone.πCategoryTheory.Limits.FormalCoproduct.cechIsoCechNerveApp · cited by 6FormalCoproduct.cechIsoCe…CategoryTheory.Limits.WidePullbackCone.IsLimit.lift · cited by 5IsLimit.liftCategoryTheory.Limits.WidePullbackShape.equivalenceOfEquiv · cited by 4WidePullbackShape.equival…CategoryTheory.CechNerveTerminalFrom.wideCospan · cited by 4CechNerveTerminalFrom.wid…CategoryTheory.Subobject.wideCospan · cited by 4Subobject.wideCospanCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Limits.WidePullbackShape · cited by 94Limits.WidePullbackShapeCategoryTheory.Limits.WidePullbackShape.Hom.casesOn · cited by 1Hom.casesOnWidePullbackShape.wideCospanCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by42

Results whose statement or proof uses this declaration.