Theorems · Definition · category theory

CategoryTheory.Functor.whiskeringLeft

(C : Type u₁) →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    (D : Type u₂) →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (E : Type u₃) →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} E] →
            CategoryTheory.Functor (CategoryTheory.Functor C D)
              (CategoryTheory.Functor (CategoryTheory.Functor D E) (CategoryTheory.Functor C E))

Left-composition gives a functor (C ⥤ D) ⥤ ((D ⥤ E) ⥤ (C ⥤ E)). (whiskeringLeft.obj F).obj G is F ⋙ G, and (whiskeringLeft.obj F).map α is whiskerLeft F α.

Defined in

Mathlib.CategoryTheory.Whiskering

Cited by

395 results in Mathlib

Foundations

Depth 26 from the axioms, rests on 107 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category