Theorems · Definition · category theory

PresheafOfModules.colimitAdjunction

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.LocallySmall.{w, v, u} C] →
      [inst_2 : CategoryTheory.IsCofiltered C] →
        [inst_3 : CategoryTheory.InitiallySmall C] →
          {R : CategoryTheory.Functor Cᵒᵖ RingCat} →
            {cR : CategoryTheory.Limits.Cocone R} →
              (hcR : CategoryTheory.Limits.IsColimit cR) →
                PresheafOfModules.colimitFunctor hcR ⊣ PresheafOfModules.constFunctor cR

Given a presheaf of rings R on a cofiltered category, this is the adjunction between colimitFunctor : PresheafOfModules R ⥤ ModuleCat cR.pt and the constant functor.

Defined in

Mathlib.Algebra.Category.ModuleCat.Presheaf.ColimitFunctor

Cited by

2 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmallCategoryTheory.IsCofilteredCategoryTheory.InitiallySmall