Mathlib Map

Theorems · Definition · category theory

CategoryTheory.Limits.Cofan.IsColimit.desc

{β : Type w} →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v, u} C] →
      {F : β → C} →
        {c : CategoryTheory.Limits.Cofan F} →
          CategoryTheory.Limits.IsColimit c → {A : C} → ((i : β) → F i ⟶ A) → (c.pt ⟶ A)

Constructor for morphisms from the point of a colimit cofan.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Products
Cited by
24 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Limits.MultispanIndex.fstSigmaMapOfIsColimit · cited by 29MultispanIndex.fstSigmaMa…CategoryTheory.Limits.MultispanIndex.sndSigmaMapOfIsColimit · cited by 29MultispanIndex.sndSigmaMa…SheafOfModules.freeHomEquiv · cited by 20SheafOfModules.freeHomEqu…CategoryTheory.Limits.Cofan.IsColimit.fac · cited by 17IsColimit.facCategoryTheory.SimplicialObject.Splitting.desc · cited by 12Splitting.descCategoryTheory.PreZeroHypercover.sigmaOfIsColimit · cited by 9PreZeroHypercover.sigmaOf…CategoryTheory.PreOneHypercover.sigmaOfIsColimit · cited by 6PreOneHypercover.sigmaOfI…CategoryTheory.Limits.Multicofork.toSigmaCofork · cited by 5Multicofork.toSigmaCoforkCategoryTheory.Limits.MonoCoprod.binaryCofanSum · cited by 4MonoCoprod.binaryCofanSumCategoryTheory.Limits.MonoCoprod.isColimitBinaryCofanSum · cited by 4MonoCoprod.isColimitBinar…CategoryTheory.GradedObject.mapBifunctor₁₂BifunctorDesc · cited by 3GradedObject.mapBifunctor…CategoryTheory.GradedObject.mapBifunctorBifunctor₂₃Desc · cited by 3GradedObject.mapBifunctor…CategoryTheory.PreOneHypercover.forkOfIsColimit · cited by 3PreOneHypercover.forkOfIs…CategoryTheory.Limits.Cofan.IsColimit.fac_assoc · cited by 2IsColimit.fac_assocCategoryTheory.GrothendieckTopology.ofArrows_mem_iff_isLocallySurjective_cofanIsColimitDesc_shrinkYoneda_map · cited by 2GrothendieckTopology.ofAr…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Limits.Cocone.pt · cited by 1354Cocone.ptCategoryTheory.Limits.IsColimit · cited by 773Limits.IsColimitCategoryTheory.Discrete.functor · cited by 633Discrete.functorCategoryTheory.Limits.IsColimit.desc · cited by 144IsColimit.descCategoryTheory.Limits.Cofan · cited by 124Limits.CofanCategoryTheory.Limits.Cofan.mk · cited by 105Cofan.mkIsColimit.descCITED BYCITES

Cites9

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Cited by43

Results whose statement or proof uses this declaration.