Theorems · Definition · category theory
CategoryTheory.Limits.colimit.cocone
{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.Cocone FAn arbitrary choice of colimit cocone of a functor.
- Defined in
- Mathlib.CategoryTheory.Limits.HasLimits
- Cited by
- 136 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 9 definitions · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.Limits.Coconestatement · cited by 746
- CategoryTheory.Limits.HasColimitstatement and proof · cited by 307
- CategoryTheory.Limits.ColimitCocone.coconeproof · cited by 42
- CategoryTheory.Limits.getColimitCoconeproof · cited by 5
Cited by183
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.colimitproof · cited by 453
- CategoryTheory.Limits.colimit.ιproof · cited by 397
- CategoryTheory.Limits.colimit.isColimitstatement · cited by 193
- CategoryTheory.Limits.colimMapproof · cited by 69
- CategoryTheory.Limits.cokernel.conditionproof · cited by 50
- CategoryTheory.Limits.ι_colimMapproof · cited by 43
- CategoryTheory.Limits.colimit.preproof · cited by 31
- CategoryTheory.Limits.coproductIsCoproductproof · cited by 31
- AlgebraicTopology.DoldKan.Γ₀.splittingproof · cited by 31
- CategoryTheory.Limits.pushout.hom_extproof · cited by 30
- CategoryTheory.Limits.colimit.wproof · cited by 24
- CategoryTheory.Limits.cokernelIsCokernelproof · cited by 23