Theorems · Definition · category theory
CategoryTheory.Limits.asEmptyCone
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] → C → CategoryTheory.Limits.Cone (CategoryTheory.Functor.empty C)Construct a cone for the empty diagram given an object.
- Cited by
- 12 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.Conestatement · cited by 710
- CategoryTheory.Functor.emptystatement · cited by 103
- CategoryTheory.Discrete.casesOnproof · cited by 90
Cited by28
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.IsTerminal.fromproof · cited by 160
- CategoryTheory.Limits.IsTerminalproof · cited by 153
- CategoryTheory.Limits.terminal.fromproof · cited by 77
- CategoryTheory.Over.cartesianMonoidalCategoryproof · cited by 68
- CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryOverproof · cited by 49
- CategoryTheory.CartesianMonoidalCategory.preservesTerminalIsoproof · cited by 8
- CategoryTheory.Limits.IsTerminal.hasTerminalproof · cited by 6
- CategoryTheory.Limits.isLimitEquivIsTerminalOfIsEmptyproof · cited by 2
- AddCommGrpCat.cartesianMonoidalCategoryproof · cited by 2
- CategoryTheory.Over.rightUnitor_inv_left_fstproof · cited by 2
- CategoryTheory.SemilatticeInf.cartesianMonoidalCategoryproof · cited by 2
- CategoryTheory.Limits.isLimitMapConeEmptyConeEquivstatement and proof · cited by 1