Theorems · Definition · category theory

CategoryTheory.flipCompEvaluation

{A : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} A] →
    {B : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} B] →
        {C : Type u₃} →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} C] →
            (F : CategoryTheory.Functor A (CategoryTheory.Functor B C)) →
              (a : A) → F.flip.comp ((CategoryTheory.evaluation A C).obj a) ≅ F.obj a

F.flip composed with evaluation is the same as evaluating F.

Defined in

Mathlib.CategoryTheory.Products.Basic

Cited by

12 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category