Theorems · Definition · category theory

PresheafOfModules.constFunctor

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

Given a cocone cR for a functor R : Cᵒᵖ ⥤ RingCat, this is the functor ModuleCat cR.pt ⥤ PresheafOfModules R which sends a module M over cR.pt to a presheaf of modules whose underlying presheaf of abelian groups is the constant functor Cᵒᵖ ⥤ AddCommGrpCat with value M.

Defined in

Mathlib.Algebra.Category.ModuleCat.Presheaf.ColimitFunctor

Cited by

7 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category