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Theorems · Definition · category theory

CategoryTheory.Limits.WidePushoutShape.wideSpan

{J : Type w} →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v, u} C] →
      (B : C) →
        (objs : J → C) → ((j : J) → B ⟶ objs j) → CategoryTheory.Functor (CategoryTheory.Limits.WidePushoutShape J) C

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

Defined in
Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks
Cited by
8 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.span · cited by 294Limits.spanCategoryTheory.Limits.HasWidePushout · cited by 33Limits.HasWidePushoutCategoryTheory.Limits.widePushout · cited by 20Limits.widePushoutCategoryTheory.Limits.WidePushout.head · cited by 13WidePushout.headCategoryTheory.Limits.WidePushout.ι · cited by 13WidePushout.ιCategoryTheory.Limits.WidePushout.desc · cited by 10WidePushout.descCategoryTheory.Limits.WidePushout.arrow_ι · cited by 2WidePushout.arrow_ιCategoryTheory.Limits.WidePushoutShape.equivalenceOfEquiv · cited by 1WidePushoutShape.equivale…CategoryTheory.Limits.Concrete.widePushout_exists_rep · cited by 1Concrete.widePushout_exis…RingHom.EssFiniteType.exists_eq_comp_ι_app_of_isColimit · cited by 1EssFiniteType.exists_eq_c…CategoryTheory.Limits.WidePushoutShape.diagramIsoWideSpan · cited by 0WidePushoutShape.diagramI…CategoryTheory.Limits.WidePushoutShape.wideSpan_map · cited by 0WidePushoutShape.wideSpan…CategoryTheory.Limits.WidePushoutShape.wideSpan_obj · cited by 0WidePushoutShape.wideSpan…CategoryTheory.Limits.Concrete.widePushout_exists_rep' · cited by 0Concrete.widePushout_exis…CategoryTheory.Limits.WidePushout.eq_desc_of_comp_eq · cited by 0WidePushout.eq_desc_of_co…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Limits.WidePushoutShape · cited by 47Limits.WidePushoutShapeCategoryTheory.Limits.WidePushoutShape.Hom.casesOn · cited by 2Hom.casesOnWidePushoutShape.wideSpanCITED BYCITES

Cites6

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

Cited by16

Results whose statement or proof uses this declaration.