Theorems · Definition · category theory

CategoryTheory.Functor.partialLeftAdjointHomEquiv

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (F : CategoryTheory.Functor D C) →
          {X : F.PartialLeftAdjointSource} → {Y : D} → (F.partialLeftAdjointObj X ⟶ Y) ≃ (X.obj ⟶ F.obj Y)

Given F : D ⥤ C, this is the canonical bijection (F.partialLeftAdjointObj X ⟶ Y) ≃ (X.obj ⟶ F.obj Y) for all X : F.PartialLeftAdjointSource and Y : D.

Defined in

Mathlib.CategoryTheory.Adjunction.PartialAdjoint

Cited by

7 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category