Theorems · Definition · category theory

CategoryTheory.Functor.functorHom

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {D : Type u'} →
      [inst_1 : CategoryTheory.Category.{v', u'} D] →
        CategoryTheory.Functor C D → CategoryTheory.Functor C D → CategoryTheory.Functor C (Type (max v' v u))

Composition of homObjFunctor with the co-Yoneda embedding, i.e. Hom(F ⊗ coyoneda(-), G). When F G : C ⥤ Type max v' v u, this is the internal hom of F and G: see Mathlib/CategoryTheory/Closed/FunctorToTypes.lean.

Defined in

Mathlib.CategoryTheory.Functor.FunctorHom

Cited by

16 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Category