Theorems · Definition · category theory
CategoryTheory.Limits.asEmptyCocone
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] → C → CategoryTheory.Limits.Cocone (CategoryTheory.Functor.empty C)Construct a cocone for the empty diagram given an object.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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.Discretestatement and proof · cited by 2,447
- CategoryTheory.Limits.Coconestatement · cited by 746
- CategoryTheory.Functor.emptystatement · cited by 103
- CategoryTheory.Discrete.casesOnproof · cited by 90
Cited by14
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.IsInitialproof · cited by 158
- CategoryTheory.Limits.IsInitial.toproof · cited by 119
- CategoryTheory.Limits.initial.toproof · cited by 63
- CategoryTheory.Limits.IsInitial.hasInitialproof · cited by 7
- CategoryTheory.Limits.isColimitEquivIsInitialOfIsEmptyproof · cited by 2
- CategoryTheory.isVanKampenColimit_of_isEmptyproof · cited by 2
- CategoryTheory.Limits.isColimitMapCoconeEmptyCoconeEquivstatement and proof · cited by 1
- CategoryTheory.StructuredArrow.mkIdInitialproof · cited by 1
- CategoryTheory.IsInitial.isVanKampenColimitstatement and proof · cited by 1
- CategoryTheory.mkInitialOfLeftAdjointproof · cited by 1
- CategoryTheory.Functor.isInitialproof · cited by 0
- CategoryTheory.Limits.hasInitial_of_hasInitial_of_preservesColimitproof · cited by 0