Theorems · Inductive type · category theory

CategoryTheory.Limits.Cone

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u₃} →
      [inst_1 : CategoryTheory.Category.{v₃, u₃} C] → CategoryTheory.Functor J C → Type (max (max u₁ u₃) v₃)

A c : Cone F is: * an object c.pt and * a natural transformation c.π : c.pt ⟶ F from the constant c.pt functor to F. Example: if J is a category coming from a poset then the data required to make a term of type Cone F is morphisms πⱼ : c.pt ⟶ F j for all j : J and, for all i ≤ j in J, morphisms πᵢⱼ : F i ⟶ F j such that πᵢ ≫ πᵢⱼ = πⱼ. Cone F is equivalent, via cone.equiv below, to Σ X, F.cones.obj X.

Defined in

Mathlib.CategoryTheory.Limits.Cones

Cited by

710 results in Mathlib

Foundations

Depth 2 from the axioms, rests on 3 definitions · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category