Theorems · Definition · category theory

CategoryTheory.FunctorToTypes.functorHomEquiv

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (F G H : CategoryTheory.Functor C (Type (max w v u))) →
      (G ⟶ F.functorHom H) ≃ (CategoryTheory.MonoidalCategoryStruct.tensorObj F G ⟶ H)

When F G H : C ⥤ Type max w v u, we have (G ⟶ F.functorHom H) ≃ (F ⊗ G ⟶ H).

Defined in: Mathlib.CategoryTheory.Monoidal.Closed.FunctorToTypes
Cited by: 2 results in Mathlib
Foundations: Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement · cited by 32,603
CategoryTheory.Functorstatement and proof · cited by 16,252
Equivstatement · cited by 8,337
CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
Equiv.transproof · cited by 337
CategoryTheory.Functor.functorHomstatement · cited by 16
CategoryTheory.Functor.homObjEquivproof · cited by 3
CategoryTheory.Functor.functorHomEquivproof · cited by 2

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.FunctorToTypes.functorHomEquiv_apply_appstatement and proof · cited by 0
CategoryTheory.FunctorToTypes.functorHomEquiv_symm_apply_appstatement and proof · cited by 0
CategoryTheory.FunctorToTypes.adjproof · cited by 0