Theorems · Definition · category theory

CategoryTheory.WithInitial.mkCommaObject

{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.WithInitial C) D →
          CategoryTheory.Comma (CategoryTheory.Functor.const C) (CategoryTheory.Functor.id (CategoryTheory.Functor C D))

A functor WithInitial C ⥤ D can be seen as an element of the comma category Comma (const C) (𝟭 (C ⥤ D)).

Defined in

Mathlib.CategoryTheory.WithTerminal.Basic

Cited by

22 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category