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Theorems · Theorem · category theory

CochainComplex.HomComplex.Cochain.v.congr_simp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  {F G : CochainComplex C ℤ} {n : ℤ} (γ γ_1 : CochainComplex.HomComplex.Cochain F G n),
  γ = γ_1 → ∀ (p q : ℤ) (hpq : p + n = q), γ.v p q hpq = γ_1.v p q hpq
Defined in
Mathlib.Algebra.Homology.HomotopyCategory.HomComplex
Cited by
38 results in Mathlib
Foundations
Depth 40 from the axioms · uses propext
Assumes
CategoryTheory.CategoryCategoryTheory.Preadditive

Around this declaration

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CochainComplex.mappingCone.inr_f_fst_v · cited by 9mappingCone.inr_f_fst_vCochainComplex.mappingCone.inr_f_desc_f · cited by 8mappingCone.inr_f_desc_fCochainComplex.mappingCone.inl_v_fst_v · cited by 7mappingCone.inl_v_fst_vCochainComplex.mappingCone.inr_f_triangle_mor₃_f · cited by 6mappingCone.inr_f_triangl…CochainComplex.mappingCone.inl_v_desc_f · cited by 5mappingCone.inl_v_desc_fCochainComplex.mappingCone.inl_v_triangle_mor₃_f · cited by 5mappingCone.inl_v_triangl…CochainComplex.mappingCone.lift_f_snd_v · cited by 3mappingCone.lift_f_snd_vCochainComplex.mappingCone.lift_f_fst_v · cited by 2mappingCone.lift_f_fst_vCochainComplex.mappingCocone.lift_f_fst_f · cited by 2mappingCocone.lift_f_fst_fCochainComplex.mappingConeCompHomotopyEquiv_comm₂ · cited by 2CochainComplex.mappingCon…CochainComplex.MappingConeCompHomotopyEquiv.hom_inv_id · cited by 2MappingConeCompHomotopyEq…CochainComplex.HomComplex.Cocycle.ofHom_homOf_eq_self · cited by 1Cocycle.ofHom_homOf_eq_se…CochainComplex.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_fCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveHomologicalComplex.X · cited by 1839HomologicalComplex.XComplexShape.up · cited by 1123ComplexShape.upCochainComplex · cited by 1016CochainComplexCochainComplex.HomComplex.Cochain · cited by 341HomComplex.CochainCochainComplex.HomComplex.Cochain.v · cited by 213Cochain.vv.congr_simpCITED BYCITES

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Cited by38

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