Theorems · Definition · category theory

SheafOfModules.isColimitFreeCofan

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      {R : CategoryTheory.Sheaf J RingCat} →
        [inst_1 : CategoryTheory.HasWeakSheafify J AddCommGrpCat] →
          [inst_2 : J.WEqualsLocallyBijective AddCommGrpCat] →
            (I : Type u) → CategoryTheory.Limits.IsColimit (SheafOfModules.freeCofan I)

free I is the colimit of copies of unit R indexed by I.

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.Free

Cited by

4 results in Mathlib

Foundations

Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasWeakSheafifyCategoryTheory.GrothendieckTopology.WEqualsLocallyBijective