Theorems · Definition · category theory
CategoryTheory.Limits.getColimitCocone
{J : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} J] →
{C : Type u} →
[inst_1 : CategoryTheory.Category.{v, u} C] →
(F : CategoryTheory.Functor J C) → [CategoryTheory.Limits.HasColimit F] → CategoryTheory.Limits.ColimitCocone FUse the axiom of choice to extract explicit ColimitCocone F from HasColimit F.
- Defined in
- Mathlib.CategoryTheory.Limits.HasLimits
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses Classical.choice
Around this declaration
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.HasColimitstatement and proof · cited by 307
- CategoryTheory.Limits.ColimitCoconestatement · cited by 20
- CategoryTheory.Limits.HasColimit.exists_colimitproof · cited by 0
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.colimit.isColimitproof · cited by 193
- CategoryTheory.Limits.colimit.coconeproof · cited by 136
- CategoryTheory.IsVanKampenColimit.map_reflectiveproof · cited by 2
- CategoryTheory.Functor.Final.hasColimit_of_compproof · cited by 2
- CategoryTheory.Limits.ColimitPresentation.colimitproof · cited by 1
- CategoryTheory.Limits.inl_eq_inr_of_epi_eqproof · cited by 1
- Under.hasColimit_of_hasColimit_liftFromUnderproof · cited by 0
- CategoryTheory.FinitaryPreExtensive.hasPullbacks_of_is_coproductproof · cited by 0