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Theorems · Definition · category theory

CategoryTheory.HasExt

(C : Type u) → [inst : CategoryTheory.Category.{v, u} C] → [CategoryTheory.Abelian C] → Prop

The property that morphisms between single complexes in arbitrary degrees are w-small in the derived category.

Defined in
Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic
Cited by
218 results in Mathlib
Foundations
Depth 94 from the axioms, rests on 2,467 definitions · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Abelian

Around this declaration

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

CategoryTheory.Abelian.Ext · cited by 191Abelian.ExtCategoryTheory.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.HasExt.standard · cited by 22HasExt.standardCategoryTheory.Abelian.Ext.mk₀_hom · cited by 20Ext.mk₀_homCategoryTheory.ProjectiveResolution.extEquivCohomologyClass · cited by 19ProjectiveResolution.extE…CategoryTheory.InjectiveResolution.extEquivCohomologyClass · cited by 19InjectiveResolution.extEq…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.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianComplexShape.up · cited by 1123ComplexShape.upCochainComplex.singleFunctor · cited by 111CochainComplex.singleFunc…HomologicalComplex.quasiIso · cited by 42HomologicalComplex.quasiI…CategoryTheory.Localization.HasSmallLocalizedShiftedHom · cited by 41Localization.HasSmallLoca…CategoryTheory.HasExtCITED BYCITES

Cites7

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

Cited by267

Results whose statement or proof uses this declaration.

Showing the 200 most cited of 267.