Theorems · Definition · category theory

CategoryTheory.Limits.Cone.pt

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u₃} →
      [inst_1 : CategoryTheory.Category.{v₃, u₃} C] →
        {F : CategoryTheory.Functor J C} → CategoryTheory.Limits.Cone F → C

An object of C

Defined in: Mathlib.CategoryTheory.Limits.Cones
Cited by: 1,298 results in Mathlib
Foundations: Depth 3 from the axioms, rests on 4 definitions · uses no axioms
Assumes: CategoryTheory.Category CategoryTheory.Category

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Cites3

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 and proof · cited by 710

Cited by1,888

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.Cone.πstatement · cited by 500
CategoryTheory.Limits.limitproof · cited by 346
CategoryTheory.Limits.limit.lift_πstatement · cited by 266
CategoryTheory.Limits.IsLimit.liftstatement · cited by 167
CategoryTheory.Limits.ConeMorphism.homstatement · cited by 164
CategoryTheory.Limits.Fork.ιstatement · cited by 162
CategoryTheory.Limits.PullbackCone.fststatement · cited by 118
CategoryTheory.Limits.PullbackCone.sndstatement · cited by 113
CategoryTheory.Limits.limit.lift_π_assocstatement · cited by 95
CategoryTheory.Limits.Cone.postcomposeproof · cited by 77
CategoryTheory.Limits.IsLimit.facstatement · cited by 67
CategoryTheory.Limits.IsLimit.conePointUniqueUpToIsostatement · cited by 57

Showing the 200 most cited of 1,888.