Theorems · Definition · category theory

CategoryTheory.Sheaf.H.map

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      [inst_1 : CategoryTheory.HasSheafify J AddCommGrpCat] →
        [inst_2 : CategoryTheory.HasExt (CategoryTheory.Sheaf J AddCommGrpCat)] →
          {F G : CategoryTheory.Sheaf J AddCommGrpCat} → (F ⟶ G) → (n : ℕ) → F.H n →+ G.H n

Given a morphism of sheaves f : F ⟶ G, H.map f n is the induced additive map on cohomology groups H F n →+ H G n

Defined in

Mathlib.CategoryTheory.Sites.SheafCohomology.Basic

Cited by

9 results in Mathlib

Foundations

Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasSheafifyCategoryTheory.HasExt