Theorems · Definition · category theory

CategoryTheory.Limits.IsColimit.uniqueUpToIso

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u₃} →
      [inst_1 : CategoryTheory.Category.{v₃, u₃} C] →
        {F : CategoryTheory.Functor J C} →
          {s t : CategoryTheory.Limits.Cocone F} →
            CategoryTheory.Limits.IsColimit s → CategoryTheory.Limits.IsColimit t → (s ≅ t)

Colimit cocones on F are unique up to isomorphism.

Defined in: Mathlib.CategoryTheory.Limits.IsLimit
Cited by: 13 results in Mathlib
Foundations: Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category

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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
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.Limits.IsColimitstatement and proof · cited by 773
CategoryTheory.Limits.Coconestatement and proof · cited by 746
CategoryTheory.Limits.IsColimit.descCoconeMorphismproof · cited by 17

Cited by17

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIsoproof · cited by 67
CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_homproof · cited by 45
CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_invproof · cited by 21
CategoryTheory.Limits.preservesColimit_of_preserves_colimit_coconeproof · cited by 17
CategoryTheory.Limits.IsColimit.uniqueUpToIso_homstatement and proof · cited by 3
CategoryTheory.Limits.IsColimit.uniqueUpToIso_invstatement and proof · cited by 3
CategoryTheory.finitaryExtensive_of_preserves_and_reflectsproof · cited by 2
CategoryTheory.Limits.CoproductDisjoint.of_cofanproof · cited by 2
CategoryTheory.FinitaryExtensive.isVanKampen_finiteCoproducts_Finproof · cited by 1
CategoryTheory.FinitaryPreExtensive.isUniversal_finiteCoproducts_Finproof · cited by 1
CategoryTheory.Limits.cokernel.ofEpiproof · cited by 1
CategoryTheory.Limits.IsIPCOfShape.of_forall_existsproof · cited by 1