Theorems · Theorem · category theory

PresheafOfModules.colimitAdjunction_homEquiv

∀ {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) (F : PresheafOfModules R) (G : ModuleCat ↑cR.pt),
  (PresheafOfModules.colimitAdjunction hcR).homEquiv F G =
    ↑(PresheafOfModules.ModuleColimit.homEquiv hcR (CategoryTheory.Limits.colimit.isColimit F.presheaf))

Defined in

Mathlib.Algebra.Category.ModuleCat.Presheaf.ColimitFunctor

Cited by

1 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmallCategoryTheory.IsCofilteredCategoryTheory.InitiallySmall