Theorems · Definition · category theory

CategoryTheory.Functor.cocones

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

If F : J ⥤ C then F.cocones is the functor assigning to an object (X : C) the type of natural transformations from F to the constant functor with value X. An object corepresenting this functor is a colimit of F.

Defined in

Mathlib.CategoryTheory.Limits.Cones

Cited by

9 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category