Theorems · Definition · category theory

CategoryTheory.Limits.colimit.isoColimitCocone

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u} →
      [inst_1 : CategoryTheory.Category.{v, u} C] →
        {F : CategoryTheory.Functor J C} →
          [inst_2 : CategoryTheory.Limits.HasColimit F] →
            (t : CategoryTheory.Limits.ColimitCocone F) → CategoryTheory.Limits.colimit F ≅ t.cocone.pt

Given any other colimit cocone for F, the chosen colimit F is isomorphic to the cocone point.

Defined in: Mathlib.CategoryTheory.Limits.HasLimits
Cited by: 18 results in Mathlib
Foundations: Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Limits.HasColimit

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

Cites11

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
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.Limits.Cocone.ptstatement · cited by 1,354
CategoryTheory.Limits.colimitstatement · cited by 453
CategoryTheory.Limits.HasColimitstatement and proof · cited by 307
CategoryTheory.Limits.colimit.isColimitproof · cited by 193
CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIsoproof · cited by 67
CategoryTheory.Limits.ColimitCocone.coconestatement · cited by 42
CategoryTheory.Limits.ColimitCocone.isColimitproof · cited by 23
CategoryTheory.Limits.ColimitCoconestatement and proof · cited by 20

Cited by51

Results whose statement or proof uses this declaration.

CategoryTheory.IsPushout.isoPushoutproof · cited by 57
CategoryTheory.Limits.colimit.isoColimitCocone_ι_homstatement · cited by 27
CategoryTheory.FunctorToTypes.binaryCoproductIsoproof · cited by 10
CategoryTheory.Limits.Types.binaryCoproductIsoproof · cited by 9
CategoryTheory.Limits.colimit.isoColimitCocone_ι_invstatement · cited by 8
coprodIsoPushoutproof · cited by 8
AlgebraicGeometry.coprodMkproof · cited by 6
CategoryTheory.Limits.FormalCoproduct.coproductIsoCofanPtproof · cited by 6
CategoryTheory.Limits.pushoutZeroZeroIsoproof · cited by 5
ModuleCat.cokernelIsoRangeQuotientproof · cited by 5
CategoryTheory.Limits.Types.coequalizerIsoproof · cited by 4
CategoryTheory.Limits.Types.coproductIsoproof · cited by 4