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Theorems · Definition · category theory

CategoryTheory.Abelian.Ext

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Abelian C] → [CategoryTheory.HasExt C] → C → C → ℕ → Type w

An Ext-group in an abelian category C, defined as a Type w when [HasExt.{w} C].

Defined in
Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic
Cited by
191 results in Mathlib
Foundations
Depth 95 from the axioms, rests on 2,796 definitions · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasExt

Around this declaration

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

CategoryTheory.Abelian.Ext.mk₀ · cited by 94Ext.mk₀CategoryTheory.Abelian.Ext.comp · cited by 80Ext.compCategoryTheory.Abelian.Ext.hom · cited by 42Ext.homCategoryTheory.ShortComplex.ShortExact.extClass · cited by 36ShortExact.extClassCategoryTheory.Abelian.Ext.ext · cited by 31Ext.extCategoryTheory.Abelian.Ext.comp_hom · cited by 27Ext.comp_homCategoryTheory.InjectiveResolution.extEquivCohomologyClass · cited by 19InjectiveResolution.extEq…CategoryTheory.ProjectiveResolution.extEquivCohomologyClass · cited by 19ProjectiveResolution.extE…CategoryTheory.Abelian.Ext.postcomp · cited by 18Ext.postcompCategoryTheory.Abelian.Ext.mapExactFunctor · cited by 15Ext.mapExactFunctorCategoryTheory.Abelian.Ext.precomp · cited by 15Ext.precompCategoryTheory.Abelian.Ext.homEquiv₀ · cited by 13Ext.homEquiv₀CategoryTheory.Abelian.Ext.addEquiv₀ · cited by 12Ext.addEquiv₀CategoryTheory.Abelian.Ext.comp.congr_simp · cited by 12comp.congr_simpCategoryTheory.Sheaf.H · cited by 11Sheaf.HCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianComplexShape.up · cited by 1123ComplexShape.upCategoryTheory.HasExt · cited by 218CategoryTheory.HasExtCochainComplex.singleFunctor · cited by 111CochainComplex.singleFunc…HomologicalComplex.quasiIso · cited by 42HomologicalComplex.quasiI…CategoryTheory.Localization.SmallShiftedHom · cited by 36Localization.SmallShifted…Abelian.ExtCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by229

Results whose statement or proof uses this declaration.

Showing the 200 most cited of 229.