Theorems · Definition · category theory

CategoryTheory.Limits.LimitCone.cone

{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.LimitCone F → CategoryTheory.Limits.Cone F

The cone itself

Defined in: Mathlib.CategoryTheory.Limits.HasLimits
Cited by: 72 results in Mathlib
Foundations: Depth 3 from the axioms · uses no axioms
Assumes: CategoryTheory.Category CategoryTheory.Category

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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites4

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.Conestatement · cited by 710
CategoryTheory.Limits.LimitConestatement and proof · cited by 25

Cited by85

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.limit.coneproof · cited by 97
CategoryTheory.Limits.LimitCone.isLimitstatement · cited by 58
CategoryTheory.Limits.limit.isoLimitCone_inv_πstatement and proof · cited by 26
CategoryTheory.Limits.limit.isoLimitConestatement · cited by 8
CategoryTheory.Limits.limit.isoLimitCone_hom_πstatement and proof · cited by 8
CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.tensorHomproof · cited by 7
CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts.tensorObjproof · cited by 7
LightProfinite.toLightDiagramproof · cited by 3
CategoryTheory.Limits.BinaryFan.associatorOfLimitConestatement and proof · cited by 3
CategoryTheory.Functor.Initial.limitConeOfCompproof · cited by 3
CategoryTheory.Limits.combineConesproof · cited by 3
CategoryTheory.Functor.Initial.limitConeCompproof · cited by 2