Theorems · Definition · category theory

PresheafOfModules.freeHomEquiv

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {R : CategoryTheory.Functor Cᵒᵖ RingCat} →
      {F : CategoryTheory.Functor Cᵒᵖ (Type u)} →
        {G : PresheafOfModules R} → (PresheafOfModules.freeObj F ⟶ G) ≃ (F ⟶ G.presheaf.comp (CategoryTheory.forget Ab))

The bijection (freeObj F ⟶ G) ≃ (F ⟶ G.presheaf ⋙ forget _) when F is a presheaf of types and G a presheaf of modules.

Defined in

Mathlib.Algebra.Category.ModuleCat.Presheaf.Free

Cited by

2 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category