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Theorems · Definition · category theory

CategoryTheory.Sheaf.H

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

The cohomology of an abelian sheaf in degree n.

Defined in
Mathlib.CategoryTheory.Sites.SheafCohomology.Basic
Cited by
11 results in Mathlib
Foundations
Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.HasSheafifyCategoryTheory.HasExt

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Sheaf.H.map · cited by 9H.mapCategoryTheory.Sheaf.functorH · cited by 4Sheaf.functorHCategoryTheory.Sheaf.H.addEquiv₀_map · cited by 2H.addEquiv₀_mapCategoryTheory.Sheaf.H.equiv₀ · cited by 2H.equiv₀CategoryTheory.Sheaf.functorH_obj_coe · cited by 1Sheaf.functorH_obj_coeCategoryTheory.Sheaf.subsingleton_H_of_isZero · cited by 0Sheaf.subsingleton_H_of_i…CategoryTheory.Sheaf.functorH_map · cited by 0Sheaf.functorH_mapCategoryTheory.Sheaf.H.addEquiv₀_map_assoc · cited by 0H.addEquiv₀_map_assocCategoryTheory.Sheaf.H.equiv₀_naturality · cited by 0H.equiv₀_naturalityCategoryTheory.Sheaf.H.equiv₀_symm_naturality · cited by 0H.equiv₀_symm_naturalityCategoryTheory.Sheaf.H.map_add_apply · cited by 0H.map_add_applyCategoryTheory.Sheaf.H.map_apply · cited by 0H.map_applyCategoryTheory.Sheaf.H.map_comp_apply · cited by 0H.map_comp_applyCategoryTheory.Sheaf.H.map_id_apply · cited by 0H.map_id_applyAlgebraicGeometry.Scheme.EllAdicCohomology · cited by 0Scheme.EllAdicCohomologyCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorOpposite · cited by 8081OppositeCategoryTheory.GrothendieckTopology · cited by 1415CategoryTheory.Grothendie…CategoryTheory.Presheaf.IsSheaf · cited by 991Presheaf.IsSheafCategoryTheory.Sheaf · cited by 763CategoryTheory.SheafAddCommGrpCat · cited by 462AddCommGrpCatCategoryTheory.HasExt · cited by 218CategoryTheory.HasExtCategoryTheory.Abelian.Ext · cited by 191Abelian.ExtCategoryTheory.HasSheafify · cited by 106CategoryTheory.HasSheafifyAddCommGrpCat.of · cited by 97AddCommGrpCat.ofCategoryTheory.constantSheaf · cited by 30CategoryTheory.constantSh…Sheaf.HCITED BYCITES

Cites13

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Cited by15

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