Theorems · Definition · category theory

PresheafOfModules.colimitFunctor

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [CategoryTheory.LocallySmall.{w, v, u} C] →
      [CategoryTheory.IsCofiltered C] →
        [CategoryTheory.InitiallySmall C] →
          {R : CategoryTheory.Functor Cᵒᵖ RingCat} →
            {cR : CategoryTheory.Limits.Cocone R} →
              CategoryTheory.Limits.IsColimit cR → CategoryTheory.Functor (PresheafOfModules R) (ModuleCat ↑cR.pt)

The colimit module functor from the category of presheaves of modules over a presheaf of rings R on a cofiltered category to the category of modules over a colimit of R.

Defined in

Mathlib.Algebra.Category.ModuleCat.Presheaf.ColimitFunctor

Cited by

2 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmallCategoryTheory.IsCofilteredCategoryTheory.InitiallySmall