Theorems · Definition · category theory

CategoryTheory.WithInitial.ofCommaMorphism

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {D : Type u_1} →
      [inst_1 : CategoryTheory.Category.{v_1, u_1} D] →
        {c c' :
            CategoryTheory.Comma (CategoryTheory.Functor.const C)
              (CategoryTheory.Functor.id (CategoryTheory.Functor C D))} →
          (c ⟶ c') → (CategoryTheory.WithInitial.ofCommaObject c ⟶ CategoryTheory.WithInitial.ofCommaObject c')

A morphism in Comma (Functor.const C) (𝟭 (C ⥤ D)) gives a morphism between the associated functors WithInitial C ⥤ D.

Defined in

Mathlib.CategoryTheory.WithTerminal.Basic

Cited by

13 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category