Theorems · Definition · category theory

PresheafOfModules.isColimitFreeYonedaCoproductsCokernelCofork

{C : Type u} →
  [inst : CategoryTheory.SmallCategory C] →
    {R : CategoryTheory.Functor Cᵒᵖ RingCat} →
      (M : PresheafOfModules R) → CategoryTheory.Limits.IsColimit M.freeYonedaCoproductsCokernelCofork

If M is a presheaf of modules, the cokernel cofork M.freeYonedaCoproductsCokernelCofork is a colimit, which means that M can be expressed as a cokernel of the morphism M.toFreeYonedaCoproduct between coproducts of free presheaves of modules on Yoneda presheaves.

Defined in

Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator

Cited by

1 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.SmallCategory