Theorems · Definition · category theory

CategoryTheory.WithInitial.commaFromUnder

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {J : Type w} →
      [inst_1 : CategoryTheory.Category.{w', w} J] →
        {X : C} →
          CategoryTheory.Functor (CategoryTheory.Functor J (CategoryTheory.Under X))
            (CategoryTheory.Comma (CategoryTheory.Functor.const J)
              (CategoryTheory.Functor.id (CategoryTheory.Functor J C)))

The category of functors J ⥤ Under X can be seen as part of a comma category, namely the comma category constructed from the identity of the category of functors J ⥤ C and the functor that maps X : C to the constant functor J ⥤ C. Given a functor K : J ⥤ Under X, it is mapped to a natural transformation to the obvious functor J ⥤ C from the constant functor X.

Defined in

Mathlib.CategoryTheory.WithTerminal.Cone

Cited by

7 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category