Theorems · Definition · category theory

CategoryTheory.Functor.LeftExtension

{C : Type u_1} →
  {H : Type u_3} →
    {D : Type u_4} →
      [inst : CategoryTheory.Category.{v_1, u_1} C] →
        [inst_1 : CategoryTheory.Category.{v_3, u_3} H] →
          [inst_2 : CategoryTheory.Category.{v_4, u_4} D] →
            CategoryTheory.Functor C D →
              CategoryTheory.Functor C H → Type (max (max (max (max u_3 u_4) v_3) v_4) u_1 v_3)

Given two functors L : C ⥤ D and F : C ⥤ H, this is the category of functors F' : D ⥤ H equipped with a natural transformation F ⟶ L ⋙ F'.

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Basic

Cited by

67 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category