Theorems · Definition · category theory

CategoryTheory.WithTerminal.equivComma

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {D : Type u_1} →
      [inst_1 : CategoryTheory.Category.{v_1, u_1} D] →
        CategoryTheory.Functor (CategoryTheory.WithTerminal C) D ≌
          CategoryTheory.Comma (CategoryTheory.Functor.id (CategoryTheory.Functor C D)) (CategoryTheory.Functor.const C)

The category of functors WithTerminal C ⥤ D is equivalent to the category Comma (𝟭 (C ⥤ D)) (const C) .

Defined in

Mathlib.CategoryTheory.WithTerminal.Basic

Cited by

26 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category