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Theorems · Definition · category theory

HomologicalComplex.quasiIso

{ι : Type u_1} →
  (C : Type u) →
    [inst : CategoryTheory.Category.{v, u} C] →
      [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
        (c : ComplexShape ι) →
          [CategoryTheory.CategoryWithHomology C] → CategoryTheory.MorphismProperty (HomologicalComplex C c)

The morphism property on HomologicalComplex C c given by quasi-isomorphisms.

Defined in
Mathlib.Algebra.Homology.QuasiIso
Cited by
42 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.CategoryWithHomology

Around this declaration

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

CategoryTheory.HasExt · cited by 218CategoryTheory.HasExtCategoryTheory.Abelian.Ext · cited by 191Abelian.ExtHasDerivedCategory · cited by 190HasDerivedCategoryCategoryTheory.Abelian.Ext.mk₀ · cited by 94Ext.mk₀HasDerivedCategory.standard · cited by 42HasDerivedCategory.standa…CategoryTheory.ShortComplex.ShortExact.extClass · cited by 36ShortExact.extClassCategoryTheory.Abelian.Ext.comp_hom · cited by 27Ext.comp_homCategoryTheory.Abelian.Ext.mk₀_hom · cited by 20Ext.mk₀_homHomologicalComplexUpToQuasiIso · cited by 12HomologicalComplexUpToQua…HomologicalComplexUpToQuasiIso.Q · cited by 11HomologicalComplexUpToQua…CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHom · cited by 10CohomologyClass.toSmallSh…CategoryTheory.Abelian.Ext.homEquiv · cited by 8Ext.homEquivHomologicalComplexUpToQuasiIso.Qh · cited by 8HomologicalComplexUpToQua…HomologicalComplexUpToQuasiIso.quotientCompQhIso · cited by 7HomologicalComplexUpToQua…CochainComplex.Plus.quasiIso · cited by 6Plus.quasiIsoCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…HomologicalComplex · cited by 1691HomologicalComplexComplexShape · cited by 1684ComplexShapeCategoryTheory.CategoryWithHomology · cited by 116CategoryTheory.CategoryWi…QuasiIso · cited by 52QuasiIsoHomologicalComplex.quasiIsoCITED BYCITES

Cites8

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Cited by66

Results whose statement or proof uses this declaration.