Theorems · Inductive type · category theory
CategoryTheory.Limits.ColimitPresentation
{C : Type u} →
[CategoryTheory.Category.{v, u} C] →
(J : Type w) → [CategoryTheory.Category.{t, w} J] → C → Type (max (max (max t u) v) w)A colimit presentation of X over J is a diagram {Dᵢ} in C and natural maps
sᵢ : Dᵢ ⟶ X making X into the colimit of the Dᵢ.
- Cited by
- 54 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
Cited by97
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.ColimitPresentation.diagstatement and proof · cited by 62
- CategoryTheory.Limits.ColimitPresentation.ιstatement and proof · cited by 33
- CategoryTheory.ObjectProperty.ColimitOfShape.toColimitPresentationstatement · cited by 22
- CategoryTheory.Limits.ColimitPresentation.Totalstatement and proof · cited by 20
- CategoryTheory.Limits.ColimitPresentation.isColimitstatement and proof · cited by 19
- CategoryTheory.Limits.ColimitPresentation.Total.Homstatement · cited by 12
- CategoryTheory.ObjectProperty.indproof · cited by 11
- CategoryTheory.Limits.ColimitPresentation.Total.Hom.homstatement and proof · cited by 9
- CategoryTheory.Limits.ColimitPresentation.Total.Hom.basestatement and proof · cited by 8
- CategoryTheory.ObjectProperty.colimitsClosure_leproof · cited by 6
- CategoryTheory.Limits.ColimitPresentation.mapstatement and proof · cited by 6
- CategoryTheory.Limits.ColimitPresentation.reindexstatement and proof · cited by 6