Theorems · Definition · category theory

CategoryTheory.evaluation

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

The "evaluation at X" functor, such that (evaluation.obj X).obj F = F.obj X, which is functorial in both X and F.

Defined in

Mathlib.CategoryTheory.Products.Basic

Cited by

173 results in Mathlib

Foundations

Depth 23 from the axioms, rests on 104 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category