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Theorems · Theorem · category theory

CochainComplex.HomComplex.Cochain.ofHom_v

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  {F G : CochainComplex C ℤ} (φ : F ⟶ G) (p : ℤ), (CochainComplex.HomComplex.Cochain.ofHom φ).v p p ⋯ = φ.f p
Defined in
Mathlib.Algebra.Homology.HomotopyCategory.HomComplex
Cited by
46 results in Mathlib
Foundations
Depth 42 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.HomComplex.Cochain.comp_id · cited by 4Cochain.comp_idCochainComplex.mappingCone.inr_f_descCochain_v · cited by 4mappingCone.inr_f_descCoc…CochainComplex.mappingCocone.inr_v_descCochain_v · cited by 3mappingCocone.inr_v_descC…CochainComplex.HomComplex.Cochain.id_comp · cited by 3Cochain.id_compCochainComplex.mappingCone.inr_fst · cited by 2mappingCone.inr_fstCochainComplex.mappingCone.inr_snd · cited by 2mappingCone.inr_sndCochainComplex.mappingCocone.lift_f_fst_f · cited by 2mappingCocone.lift_f_fst_fCochainComplex.mappingConeCompHomotopyEquiv_comm₂ · cited by 2CochainComplex.mappingCon…CochainComplex.mappingCone.descShortComplex_naturality · cited by 2mappingCone.descShortComp…CochainComplex.mappingCone.inl_fst · cited by 2mappingCone.inl_fstCochainComplex.MappingConeCompHomotopyEquiv.hom_inv_id · cited by 2MappingConeCompHomotopyEq…CochainComplex.isKInjective_of_injective_aux · cited by 1CochainComplex.isKInjecti…CochainComplex.HomComplex.Cocycle.ofHom_homOf_eq_self · cited by 1Cocycle.ofHom_homOf_eq_se…CochainComplex.mappingCone.lift_desc_f · cited by 1mappingCone.lift_desc_fCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Preadditive · cited by 3309CategoryTheory.Preadditiveadd_zero · cited by 2707add_zeroHomologicalComplex.X · cited by 1839HomologicalComplex.XComplexShape.up · cited by 1123ComplexShape.upCochainComplex · cited by 1016CochainComplexHomologicalComplex.Hom.f · cited by 845Hom.fCochainComplex.HomComplex.Cochain.v · cited by 213Cochain.vCochainComplex.HomComplex.Cochain.ofHom · cited by 121Cochain.ofHomCochainComplex.HomComplex.Cochain.ofHoms_v · cited by 13Cochain.ofHoms_vCochain.ofHom_vCITED BYCITES

Cites11

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Cited by46

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