Mathlib Map

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.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.IsTerminal
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.

CategoryTheory.Limits.IsTerminal.from · cited by 160IsTerminal.fromCategoryTheory.Limits.IsTerminal · cited by 153Limits.IsTerminalCategoryTheory.Limits.terminal.from · cited by 77terminal.fromCategoryTheory.Over.cartesianMonoidalCategory · cited by 68Over.cartesianMonoidalCat…CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryOver · cited by 49ChosenPullbacksAlong.cart…CategoryTheory.CartesianMonoidalCategory.preservesTerminalIso · cited by 8CartesianMonoidalCategory…CategoryTheory.Limits.IsTerminal.hasTerminal · cited by 6IsTerminal.hasTerminalCategoryTheory.Limits.isLimitEquivIsTerminalOfIsEmpty · cited by 2Limits.isLimitEquivIsTerm…AddCommGrpCat.cartesianMonoidalCategory · cited by 2AddCommGrpCat.cartesianMo…CategoryTheory.Over.rightUnitor_inv_left_fst · cited by 2Over.rightUnitor_inv_left…CategoryTheory.SemilatticeInf.cartesianMonoidalCategory · cited by 2SemilatticeInf.cartesianM…CategoryTheory.Limits.isLimitMapConeEmptyConeEquiv · cited by 1Limits.isLimitMapConeEmpt…CategoryTheory.Over.rightUnitor_inv_left_snd · cited by 1Over.rightUnitor_inv_left…CategoryTheory.IsSifted.nonempty_of_colim_preservesLimitsOfShapeFinZero · cited by 1IsSifted.nonempty_of_coli…CategoryTheory.PreGaloisCategory.quotientByAutTerminalEquivUniqueQuotient · cited by 1PreGaloisCategory.quotien…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Limits.Cone · cited by 710Limits.ConeCategoryTheory.Functor.empty · cited by 103Functor.emptyCategoryTheory.Discrete.casesOn · cited by 90Discrete.casesOnLimits.asEmptyConeCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by28

Results whose statement or proof uses this declaration.