Theorems · Definition · category theory

CategoryTheory.Limits.ColimitCocone.isColimit

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u} →
      [inst_1 : CategoryTheory.Category.{v, u} C] →
        {F : CategoryTheory.Functor J C} →
          (self : CategoryTheory.Limits.ColimitCocone F) → CategoryTheory.Limits.IsColimit self.cocone

The proof that it is the colimit cocone

Defined in: Mathlib.CategoryTheory.Limits.HasLimits
Cited by: 23 results in Mathlib
Foundations: Depth 4 from the axioms · uses no axioms
Assumes: CategoryTheory.Category CategoryTheory.Category

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

Cites5

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.Limits.IsColimitstatement · cited by 773
CategoryTheory.Limits.ColimitCocone.coconestatement · cited by 42
CategoryTheory.Limits.ColimitCoconestatement and proof · cited by 20

Cited by34

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.colimit.isColimitproof · cited by 193
CategoryTheory.Limits.colimit.isoColimitCocone_ι_homproof · cited by 27
CategoryTheory.Limits.colimit.isoColimitCoconeproof · cited by 18
SSet.relativeCellComplexOfMonoproof · cited by 14
CategoryTheory.Limits.colimit.isoColimitCocone_ι_invproof · cited by 8
CategoryTheory.Limits.limitBiconeOfUniqueproof · cited by 7
CategoryTheory.Limits.coproductUniqueIsoproof · cited by 5
CategoryTheory.Functor.Final.colimitCoconeOfCompproof · cited by 3
CategoryTheory.Limits.combineCoconesproof · cited by 3
CategoryTheory.Limits.CompleteLattice.finite_colimit_eq_finset_univ_supproof · cited by 2
CategoryTheory.Functor.Final.colimitCoconeCompproof · cited by 2
CategoryTheory.IsVanKampenColimit.map_reflectiveproof · cited by 2