Theorems · Definition · category theory

CategoryTheory.Sheaf.cohomologyPresheaf

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      [inst_1 : CategoryTheory.HasSheafify J AddCommGrpCat] →
        [CategoryTheory.HasExt (CategoryTheory.Sheaf J AddCommGrpCat)] →
          CategoryTheory.Sheaf J AddCommGrpCat → ℕ → CategoryTheory.Functor Cᵒᵖ AddCommGrpCat

Given an abelian sheaf F, this is the presheaf which sends U to the nth Ext-group from the free abelian sheaf generated by the presheaf of sets yoneda.obj U to F.

Defined in

Mathlib.CategoryTheory.Sites.SheafCohomology.Basic

Cited by

6 results in Mathlib

Foundations

Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasSheafifyCategoryTheory.HasExt