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Theorems · Theorem · category theory

CochainComplex.HomComplex.Cocycle.homOf_f

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  {F G : CochainComplex C ℤ} (z : CochainComplex.HomComplex.Cocycle F G 0) (i : ℤ), z.homOf.f i = (↑z).v i i ⋯
Defined in
Mathlib.Algebra.Homology.HomotopyCategory.HomComplex
Cited by
13 results in Mathlib
Foundations
Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Preadditive

Around this declaration

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

CochainComplex.mappingCone.inr_f_desc_f · cited by 8mappingCone.inr_f_desc_fCochainComplex.mappingCone.inl_v_desc_f · cited by 5mappingCone.inl_v_desc_fCochainComplex.mappingCone.lift_f_snd_v · cited by 3mappingCone.lift_f_snd_vCochainComplex.mappingCocone.lift_f_fst_f · cited by 2mappingCocone.lift_f_fst_fCochainComplex.mappingCone.lift_f_fst_v · cited by 2mappingCone.lift_f_fst_vCochainComplex.HomComplex.Cocycle.ofHom_homOf_eq_self · cited by 1Cocycle.ofHom_homOf_eq_se…CochainComplex.mappingCocone.lift_f_snd_v · cited by 1mappingCocone.lift_f_snd_vCochainComplex.mappingCocone.inl_v_desc_f · cited by 1mappingCocone.inl_v_desc_fCochainComplex.mappingCocone.inr_v_desc_f · cited by 1mappingCocone.inr_v_desc_fCochainComplex.mappingCone.lift_desc_f · cited by 1mappingCone.lift_desc_fCochainComplex.mappingCocone.inr_v_fst_f · cited by 1mappingCocone.inr_v_fst_fCochainComplex.mappingCocone.id_X · cited by 0mappingCocone.id_XCochainComplex.HomComplex.Cocycle.homOf_ofHom_eq_self · cited by 0Cocycle.homOf_ofHom_eq_se…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveAddSubgroup · cited by 3232AddSubgroupHomologicalComplex.X · cited by 1839HomologicalComplex.XComplexShape.up · cited by 1123ComplexShape.upCochainComplex · cited by 1016CochainComplexHomologicalComplex.Hom.f · cited by 845Hom.fCochainComplex.HomComplex.Cochain · cited by 341HomComplex.CochainCochainComplex.HomComplex.Cochain.v · cited by 213Cochain.vCochainComplex.HomComplex.Cocycle · cited by 130HomComplex.CocycleCochainComplex.HomComplex.cocycle · cited by 105HomComplex.cocycleCochainComplex.HomComplex.Cocycle.homOf · cited by 9Cocycle.homOfCocycle.homOf_fCITED BYCITES

Cites13

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Cited by13

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