Defs

📁 Source: Mathlib/Algebra/Group/Int/Defs.lean

Statistics

Metric	Count
Definitions instAddCommGroup, instAddCommMonoid, instAddCommSemigroup, instAddGroup, instAddMonoid, instAddSemigroup, instCommMonoid, instCommSemigroup, instMonoid, instSemigroup	10
Theorems instIsAddTorsionFree, nsmul_eq_mul, zsmul_eq_mul, zsmul_int_int, zsmul_int_one	5
Total	15

Int

Definitions

Name	Category	Theorems
instAddCommGroup 📖	CompOp	191 math math: IsDedekindDomain.HeightOneSpectrum.adicValued.has_uniform_continuous_const_smul', Complex.meromorphicOrderAt_canonicalFactor, fun_meromorphicOrderAt_div, ValuationSubring.integralClosure_algebraMap_injective, Profinite.NobelingProof.injective_πs', NumberField.FinitePlace.mk_apply, AddCommGrpCat.asHom_hom_apply, CharacterModule.int.divByNat_self, Padic.withValUniformEquiv_norm_le_one_iff, IsDedekindDomain.HeightOneSpectrum.denseRange_algebraMap, Profinite.NobelingProof.Products.span_nil_eq_top, LaurentSeries.LaurentSeriesRingEquiv_def, IsDedekindDomain.HeightOneSpectrum.instFaithfulSMulSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, NumberField.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicCompletionV, Profinite.NobelingProof.GoodProducts.linearIndependent_iff_union_smaller, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, Profinite.NobelingProof.coe_πs, Set.unit_eq, NumberField.FinitePlace.norm_def', IsDedekindDomain.HeightOneSpectrum.mem_adicCompletionIntegers, Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_restrict_apply_of_surjective, NumberField.FinitePlace.embedding_apply, NumberField.HeightOneSpectrum.NumberField.toNNReal_valued_eq_adicAbv, LaurentSeries.valuation_le_iff_coeff_lt_eq_zero, instIsDiscreteValuationRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, LaurentSeries.valuation_single_zpow, List.sum_int_mod, NumberField.HeightOneSpectrum.rankOne_hom'_def, Profinite.NobelingProof.Products.max_eq_eval, Profinite.NobelingProof.Products.eval_πs, LocallyConstant.freeOfProfinite, Padic.addValuation.apply, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, univ_addEquiv, RatFunc.coe_X, IsDedekindDomain.HeightOneSpectrum.adicCompletion.instIsScalarTower', Profinite.NobelingProof.Products.eval_πs', RatFunc.coe_coe, NumberField.FinitePlace.norm_embedding_eq, LaurentSeries.inducing_coe, AddCommGrpCat.asHom_injective, LaurentSeries.continuous_coe, LaurentSeries.algebraMap_C_mem_adicCompletionIntegers, Profinite.NobelingProof.GoodProducts.spanFin, Profinite.NobelingProof.succ_exact, Profinite.NobelingProof.GoodProducts.smaller_factorization, NumberField.FinitePlace.norm_embedding, Profinite.NobelingProof.πs'_apply_apply, LaurentSeries.val_le_one_iff_eq_coe, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_def, IsDiscreteValuationRing.isRankOneDiscrete, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.integers, Rat.HeightOneSpectrum.adicCompletion.padicEquiv_bijOn, NumberField.AdeleRing.algebraMap_snd_apply, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletionIntegers_apply, Valued.tendsto_zero_pow_of_le_exp_neg_one, FunctionField.valuedFqtInfty.def, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletionIntegers, IsDedekindDomain.HeightOneSpectrum.coe_algebraMap_mem, IsDedekindDomain.HeightOneSpectrum.valuation_def, NumberField.HeightOneSpectrum.NumberField.rankOne_hom'_def, IsDedekindDomain.HeightOneSpectrum.instFaithfulSMulSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers_1, LaurentSeries.exists_ratFunc_val_lt, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, addEquiv_eq_refl_or_neg, CharacterModule.intSpanEquivQuotAddOrderOf_symm_apply_coe, NumberField.FinitePlace.norm_lt_one_iff_mem, CharacterModule.intSpanEquivQuotAddOrderOf_apply, RatFunc.valuation_surjective, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation', meromorphicOrderAt_inv, ValuationSubring.instIsScalarTowerSubtypeMemValuationSubringWithZeroMultiplicativeInt, Submodule.span_singleton_toAddSubgroup_eq_zmultiples, IsDedekindDomain.HeightOneSpectrum.instIsTorsionFreeSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, Profinite.NobelingProof.Products.eval_πs_image', NumberField.FinitePlace.IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, NumberField.FinitePlace.IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_apply, fwdDiff_choose, RatFunc.valuation_eq_LaurentSeries_valuation, PadicInt.coe_adicCompletionIntegersEquiv_apply, Profinite.NobelingProof.GoodProducts.span, Profinite.NobelingProof.GoodProducts.linearIndependent_iff_smaller, LaurentSeries.coe_X_compare, NumberField.HeightOneSpectrum.embedding_mul_absNorm, absNorm_under_mem, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, AddCommGrpCat.int_hom_ext_iff, RatFunc.algebraMap_apply_div, meromorphicOrderAt_div, PeriodPair.order_weierstrassP, fwdDiff_iter_choose_zero, LaurentSeries.exists_powerSeries_of_memIntegers, LaurentSeries.continuous_coe', NumberField.FinitePlace.equivHeightOneSpectrum_symm_apply, IsDedekindDomain.HeightOneSpectrum.adicValued_apply, NumberField.FinitePlace.norm_def_int, Profinite.NobelingProof.GoodProducts.linearIndependent_iff_sum, ValuationSubring.isIntegral_of_mem_ringOfIntegers', instIsAddTorsionFree, IsDiscreteValuationRing.map_algebraMap_eq_valuationSubring, Profinite.NobelingProof.πs_apply_apply, Profinite.NobelingProof.GoodProducts.finsuppSum_mem_span_eval, LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring, Profinite.NobelingProof.GoodProducts.linearIndependent, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation, IsDedekindDomain.HeightOneSpectrum.coe_mem_adicCompletionIntegers, Padic.toEquiv_withValUniformEquiv_eq_toEquiv_withValRingEquiv, Ideal.span_singleton_toAddSubgroup_eq_zmultiples, Profinite.NobelingProof.GoodProducts.square_commutes, LaurentSeries.valuation_LaurentSeries_equal_extension, Profinite.NobelingProof.Nobeling_aux, RatFunc.v_def, LaurentSeries.LaurentSeries_coe, Profinite.NobelingProof.spanFinBasis.span, LaurentSeries.powerSeries_ext_subring, NumberField.HeightOneSpectrum.instFiniteAdicCompletionRingOfIntegers, ValuationSubring.isIntegral_of_mem_ringOfIntegers, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, absNorm_under_dvd_absNorm, LaurentSeries.powerSeriesRingEquiv_coe_apply, PeriodPair.latticeEquiv_symm_apply, instIsDiscreteValuationRingSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, FunctionField.inftyValuedFqt.def, IsDedekindDomain.HeightOneSpectrum.adicValued.uniformContinuousConstSMul, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_surjective, LaurentSeries.instLaurentSeriesComplete, Profinite.NobelingProof.GoodProducts.linearIndependentEmpty, Padic.withValUniformEquiv_cast_apply, LaurentSeries.valuation_surjective, LaurentSeries.valuation_coe_ratFunc, Padic.coe_withValRingEquiv, NumberField.FinitePlace.norm_eq_one_iff_notMem, LaurentSeries.valuation_compare, Padic.isUniformInducing_cast_withVal, LaurentSeries.tendsto_valuation, Profinite.NobelingProof.GoodProducts.span_iff_products, LaurentSeries.coe_range_dense, IsDedekindDomain.HeightOneSpectrum.adicValued_apply', Padic.coe_withValRingEquiv_symm, IsDedekindDomain.HeightOneSpectrum.adicCompletion_valueGroup_eq, LaurentSeries.comparePkg_eq_extension, RatFunc.single_zpow, LaurentSeries.valuation_def, Profinite.NobelingProof.CC_comp_zero, Profinite.NobelingProof.eval_eq_πJ, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.isUnit_iff_valued_eq_one, Profinite.NobelingProof.CC_exact, LaurentSeries.valuation_le_iff_coeff_lt_log_eq_zero, LaurentSeries.uniformContinuous_coeff, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletion, instIsPrincipalIdealRingSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, CharacterModule.intSpanEquivQuotAddOrderOf_apply_self, LaurentSeries.ratfuncAdicComplRingEquiv_apply, Profinite.NobelingProof.injective_πs, Profinite.NobelingProof.coe_πs', IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.mem_units_iff_valued_eq_one, Set.integer_eq, ideal_span_absNorm_eq_self, sign_eq_sign, fun_meromorphicOrderAt_inv, NumberField.HeightOneSpectrum.toNNReal_valued_eq_adicAbv, NumberField.FinitePlace.norm_embedding', NumberField.FinitePlace.norm_le_one, absNorm_under_eq_sInf, LaurentSeries.mem_integers_of_powerSeries, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletion, Valuation.IsRankOneDiscrete.generator_eq_neg_exp_one_of_surjective, cast_mem_ideal_iff, ValuationSubring.algebraMap_injective, Profinite.NobelingProof.GoodProducts.linearIndependent_iff_range, IsDedekindDomain.HeightOneSpectrum.adicCompletion.mul_nonZeroDivisor_mem_adicCompletionIntegers, RatFunc.single_inv, Profinite.NobelingProof.GoodProducts.max_eq_eval, Valued.exists_pow_lt_of_le_exp_neg_one, instIsPrincipalIdealRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, Ideal.ringChar_quot, Profinite.NobelingProof.GoodProducts.linearIndependentSingleton, liesOver_span_absNorm, Profinite.NobelingProof.Products.eval_πs_image, NumberField.FinitePlace.norm_embedding_int, LaurentSeries.exists_ratFunc_eq_v, Padic.isDenseInducing_cast_withVal, LaurentSeries.uniformContinuous_withVal_equiv, Nat.absNorm_under_prime, fwdDiff_iter_choose, LaurentSeries.valuation_X_pow, NumberField.FinitePlace.norm_def, submodule_toAddSubgroup_index_ne_zero_iff, IsDedekindDomain.HeightOneSpectrum.notMem_adicCompletionIntegers, Profinite.NobelingProof.GoodProducts.max_eq_eval_unapply, Profinite.NobelingProof.succ_mono
instAddCommMonoid 📖	CompOp	456 math math: HomotopyCategory.spectralObjectMappingCone_δ'_app, DerivedCategory.instIsLocalizationCochainComplexIntQQuasiIsoUp, CategoryTheory.ShortComplex.ShortExact.instHasSmallLocalizedShiftedHomHomologicalComplexIntUpQuasiIsoX₃CochainComplexMapSingleFunctorOfNatX₁, ComplexShape.embeddingUpIntDownInt_f, CochainComplex.mappingConeCompTriangleh_comm₁_assoc, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app, IsDedekindDomain.HeightOneSpectrum.adicValued.has_uniform_continuous_const_smul', LaurentPolynomial.mk'_one_X_pow, sum_modEq_single, ValuationSubring.integralClosure_algebraMap_injective, LaurentPolynomial.mk'_mul_T, ModEq.multisetSum_map_zero, Profinite.NobelingProof.injective_πs', qExpansionRingHom_apply, Padic.withValUniformEquiv_norm_le_one_iff, Rat.padicValuation_cast, HomologicalComplex₂.totalShift₂Iso_hom_naturality_assoc, CategoryTheory.InjectiveResolution.ι'_f_zero, IsDedekindDomain.HeightOneSpectrum.intValuation_eq_one_iff_mem_primeCompl, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₁, Profinite.NobelingProof.Products.span_nil_eq_top, WeierstrassCurve.HasAdditiveReduction.badReduction, LaurentSeries.LaurentSeriesRingEquiv_def, HomologicalComplex₂.shiftFunctor₂XXIso_refl, NumberField.instIsRankOneDiscreteWithZeroMultiplicativeIntAdicCompletionV, Profinite.NobelingProof.GoodProducts.linearIndependent_iff_union_smaller, Profinite.NobelingProof.coe_πs, CochainComplex.instIsStrictlyLEObjHomologicalComplexIntUpSingle, Set.unit_eq, Padic.instCompatibleWithZeroMultiplicativeIntMulValuation, NumberField.FinitePlace.norm_def', DerivedCategory.instCommShiftHomologicalComplexIntUpHomFunctorQuotientCompQhIso, FunctionField.inftyValuation.X_inv, Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_restrict_apply_of_surjective, padicValuation_lt_one_iff, IsDedekindDomain.HeightOneSpectrum.intValuation_if_neg, IsDedekindDomain.HeightOneSpectrum.valuation_of_algebraMap, CochainComplex.mappingCone.homologySequenceδ_triangleh, NumberField.HeightOneSpectrum.NumberField.toNNReal_valued_eq_adicAbv, LaurentPolynomial.mk'_one_X, LaurentSeries.valuation_le_iff_coeff_lt_eq_zero, instIsDiscreteValuationRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, LaurentSeries.valuation_single_zpow, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_obj, Finset.sum_Ico_le_sum, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂_assoc, alternating_sum_range_choose_of_ne, IsDedekindDomain.HeightOneSpectrum.intValuation_le_one, WeierstrassCurve.valuation_Δ_aux_eq_of_isIntegral, NumberField.HeightOneSpectrum.rankOne_hom'_def, CochainComplex.HomComplex.CohomologyClass.equivOfIsKInjective_apply, HomologicalComplex₂.D₂_totalShift₁XIso_hom_assoc, erdos_ginzburg_ziv, HomologicalComplex₂.D₂_totalShift₂XIso_hom_assoc, Profinite.NobelingProof.Products.max_eq_eval, IsDedekindDomain.HeightOneSpectrum.instIsNontrivialWithZeroMultiplicativeIntValuation, Profinite.NobelingProof.Products.eval_πs, padicValuation_eq_one_iff, ModularForm.prod_slash_sum_weights, RatFunc.valuation_isEquiv_adic_of_valuation_X_le_one, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁_assoc, LocallyConstant.freeOfProfinite, CochainComplex.shiftShortComplexFunctorIso_add'_hom_app, Finset.inclusion_exclusion_card_inf_compl, CochainComplex.instIsCompatibleWithShiftHomologicalComplexIntUpQuasiIso, CochainComplex.HomComplex.Cochain.toSingleMk_v, CochainComplex.IsKInjective.rightOrthogonal, CochainComplex.IsKInjective.Qh_map_bijective, HomotopyCategory.instIsHomologicalIntUpHomologyFunctor, IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_mem, LaurentSeries.ofPowerSeries_powerSeriesPart, IsDedekindDomain.HeightOneSpectrum.intValuation_singleton, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, LaurentSeries.single_order_mul_powerSeriesPart, FunctionField.instIsNontrivialRatFuncWithZeroMultiplicativeIntInftyValuation, DerivedCategory.homologyFunctorFactorsh_hom_app_quotient_obj_assoc, HomologicalComplex₂.ι_totalShift₁Iso_hom_f_assoc, RootPairing.Base.height_eq_sum, Rat.padicValuation_self, RatFunc.coe_X, Ring.multichoose_neg_self, CochainComplex.instIsStrictlyGEObjHomologicalComplexIntUpSingle, Profinite.NobelingProof.Products.eval_πs', LaurentSeries.coe_algebraMap, alternating_sum_range_choose, HomologicalComplex₂.ι_totalShift₁Iso_inv_f, RatFunc.coe_coe, cast_multiset_sum, Polynomial.valuation_of_mk, ComplexShape.eulerCharSignsUpInt_χ, WeierstrassCurve.hasGoodReduction_iff, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_eq, DerivedCategory.shiftMap_homologyFunctor_map_Q_assoc, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₁, LaurentSeries.inducing_coe, CochainComplex.HomComplex.CohomologyClass.bijective_toSmallShiftedHom_of_isKProjective, LaurentSeries.continuous_coe, LaurentSeries.algebraMap_C_mem_adicCompletionIntegers, alternating_sum_range_choose_eq_choose, RatFunc.adicValuation_not_isEquiv_infty_valuation, Finset.sum_int_mod, CochainComplex.HomComplex.CohomologyClass.bijective_toSmallShiftedHom_of_isKInjective, Profinite.NobelingProof.GoodProducts.spanFin, qExpansion_of_mul, CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHom_mk, HomotopyCategory.instAdditiveIntUpShiftFunctor, WeierstrassCurve.hasMultiplicativeReduction_iff, Padic.norm_eq_zpow_log_mulValuation, Profinite.NobelingProof.GoodProducts.smaller_factorization, PowerSeries.intValuation_eq_of_coe, instIsLocalizationHomologicalComplexIntUpHomotopyCategoryQuotientHomotopyEquivalences, FunctionField.instIsTrivialOnWithZeroMultiplicativeIntRatFuncInftyValuation, CategoryTheory.Functor.instCommShiftHomotopyCategoryIntUpDerivedCategoryHomMapDerivedCategoryFactorsh, HomologicalComplex₂.ι_totalShift₂Iso_inv_f_assoc, Profinite.NobelingProof.πs'_apply_apply, LaurentSeries.val_le_one_iff_eq_coe, NumberField.HeightOneSpectrum.adicAbv_def, IsDedekindDomain.HeightOneSpectrum.valuation_exists_uniformizer, MeromorphicOn.divisor_fun_prod, IsDiscreteValuationRing.isRankOneDiscrete, CochainComplex.homologyFunctor_shift, DerivedCategory.instIsTriangulatedHomotopyCategoryIntUpQh, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.integers, PowerSeries.coe_mul, Polynomial.smeval_neg_nat, Valued.tendsto_zero_pow_of_le_exp_neg_one, FunctionField.valuedFqtInfty.def, FractionalIdeal.count_prod, DerivedCategory.shiftMap_homologyFunctor_map_Qh_assoc, LaurentSeries.algebraMap_apply, quadraticChar_sum_zero, IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_dvd, HomotopyCategory.Pretriangulated.complete_distinguished_triangle_morphism, IsDedekindDomain.HeightOneSpectrum.valuation_def, HomologicalComplex₂.instHasTotalIntObjUpShiftFunctor₂, cast_finsupp_sum, NumberField.HeightOneSpectrum.NumberField.rankOne_hom'_def, Ring.multichoose_neg_succ, LaurentSeries.derivative_iterate_coeff, MeromorphicOn.divisor_prod, Finset.sum_range_le_sum, AddCommGroup.ModEq.of_intCast, LaurentSeries.exists_ratFunc_val_lt, HomotopyCategory.mappingCone_triangleh_distinguished, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj_assoc, ModularForm.levelOne_weight_zero_rank_one, CochainComplex.HomComplex.Cochain.fromSingleMk_v, Padic.mulValuation_toFun, IsDedekindDomain.HeightOneSpectrum.valuation_div_le_one_iff, RatFunc.valuation_isEquiv_valuationIdeal_adic_of_valuation_X_le_one, WeierstrassCurve.HasGoodReduction.goodReduction, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_dvd, HomologicalComplex₂.instHasTotalIntObjUpCompShiftFunctor₁ShiftFunctor₂, Padic.comap_mulValuation_eq_padicValuation, LaurentPolynomial.mk'_eq, Rat.valuation_le_one_iff_den, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₂, RatFunc.valuation_surjective, CochainComplex.HomComplex.CohomologyClass.equivOfIsKInjective_symm_apply, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app_assoc, instQFactorsThroughHomotopyIntUp, LaurentSeries.exists_Polynomial_intValuation_lt, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom, CochainComplex.instLinearHomologicalComplexIntUpShiftFunctor, DerivedCategory.instAdditiveHomotopyCategoryIntUpQh, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation', sum_modEq_ite, CategoryTheory.Functor.instCommShiftCochainComplexIntDerivedCategoryHomMapDerivedCategoryFactors, meromorphicOrderAt_fun_prod, ValuationSubring.instIsScalarTowerSubtypeMemValuationSubringWithZeroMultiplicativeInt, Submodule.span_singleton_toAddSubgroup_eq_zmultiples, CategoryTheory.ProjectiveResolution.π'_f_zero_assoc, DerivedCategory.instIsLocalizationHomotopyCategoryIntUpQhQuasiIso, HomologicalComplex₂.D₁_totalShift₂XIso_hom_assoc, HomologicalComplex₂.shiftFunctor₁XXIso_refl, cast_sum, Profinite.NobelingProof.Products.eval_πs_image', CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₃, IsDedekindDomain.HeightOneSpectrum.valuation_of_mk', LaurentSeries.of_powerSeries_localization, DerivedCategory.instHasLeftCalculusOfFractionsHomotopyCategoryIntUpQuasiIso, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_inv_f_f, RatFunc.valuation_eq_LaurentSeries_valuation, CochainComplex.mappingCone.map_inr, CategoryTheory.Functor.mapCochainComplexShiftIso_inv_app_f, HomologicalComplex₂.D₁_totalShift₁XIso_hom_assoc, HomotopyCategory.instLinearIntUpShiftFunctor, CochainComplex.HomComplex.CohomologyClass.equiv_toSmallShiftedHom_mk, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂, HomotopyCategory.Pretriangulated.distinguished_cocone_triangle, Profinite.NobelingProof.GoodProducts.span, HomologicalComplex₂.instHasTotalIntObjUpCompShiftFunctor₂ShiftFunctor₁, ModEq.multisetSum_map, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_mem, Profinite.NobelingProof.GoodProducts.linearIndependent_iff_smaller, LaurentSeries.coe_X_compare, HomotopyCategory.instLinearIntUpSingleFunctor, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, ComplexShape.eulerCharSignsDownInt_χ, HomotopyCategory.instAdditiveIntUpSingleFunctor, RatFunc.algebraMap_apply_div, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_hom_f_f, Finset.inclusion_exclusion_card_biUnion, HomotopyCategory.Pretriangulated.contractible_distinguished, range_nsmulAddMonoidHom, ComplexShape.instIsRelIffIntEmbeddingDownIntUpInt, padicValuation_self, HomologicalComplex₂.ι_totalShift₁Iso_inv_f_assoc, CategoryTheory.HasExt.hasSmallLocalizedShiftedHom_of_isLE_of_isGE, LaurentSeries.exists_powerSeries_of_memIntegers, LaurentSeries.continuous_coe', CategoryTheory.HasExt.instHasSmallLocalizedShiftedHomHomologicalComplexIntUpQuasiIsoOfIsGEOfIsLEOfNat, IsDedekindDomain.HeightOneSpectrum.adicValued_apply, NumberField.FinitePlace.norm_def_int, Profinite.NobelingProof.GoodProducts.linearIndependent_iff_sum, PowerSeries.coe_C, WeierstrassCurve.hasAdditiveReduction_iff, CochainComplex.IsKProjective.Qh_map_bijective, WeierstrassCurve.HasAdditiveReduction.additiveReduction, HomologicalComplex₂.ι_totalShift₂Iso_hom_f_assoc, ModEq.multisetSum_zero, ValuationSubring.isIntegral_of_mem_ringOfIntegers', DerivedCategory.instEssSurjHomotopyCategoryIntUpQh, CategoryTheory.ProjectiveResolution.π'_f_zero, IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_dvd, HomotopyCategory.instIsTriangulatedIntUpSubcategoryAcyclic, RatFunc.valuation_isEquiv_infty_or_adic, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_inv_app_f, IsDiscreteValuationRing.map_algebraMap_eq_valuationSubring, Profinite.NobelingProof.πs_apply_apply, HomotopyCategory.instIsTriangulatedIntUp, HomologicalComplex.eulerChar_eq_sum_finSet_of_finrankSupport_subset, numDerangements_sum, Profinite.NobelingProof.GoodProducts.finsuppSum_mem_span_eval, DerivedCategory.instFaithfulFunctorHomotopyCategoryIntUpObjWhiskeringLeftQh, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₃, HomologicalComplex₂.D₁_totalShift₁XIso_hom, IsDedekindDomain.HeightOneSpectrum.intValuation_zero_lt, HomologicalComplex₂.D₂_totalShift₁XIso_hom, LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring, Profinite.NobelingProof.GoodProducts.linearIndependent, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation, Padic.toEquiv_withValUniformEquiv_eq_toEquiv_withValRingEquiv, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₁, AddSubmonoid.isLocalizationMap_nat_int, LaurentSeries.valuation_LaurentSeries_equal_extension, Profinite.NobelingProof.Nobeling_aux, RatFunc.v_def, AddCommGroup.intCast_modEq_intCast', Rat.padicValuation_eq_zero_iff, LaurentSeries.LaurentSeries_coe, nat_abs_sum_le, IsDedekindDomain.HeightOneSpectrum.intValuation_eq_one_iff, Profinite.NobelingProof.spanFinBasis.span, exists_signed_sum', Finset.sum_powerset_neg_one_pow_card_of_nonempty, LaurentSeries.powerSeries_ext_subring, Set.unit_valuation_eq_one, ValuationSubring.isIntegral_of_mem_ringOfIntegers, HomotopyCategory.instIsCompatibleWithShiftHomologicalComplexIntUpHomotopic, AddCommGroup.modEq_iff_int_modEq, FunctionField.inftyValuation.X_zpow, CategoryTheory.InjectiveResolution.ι'_f_zero_assoc, LaurentSeries.powerSeriesRingEquiv_coe_apply, CategoryTheory.instHasSmallLocalizedShiftedHomHomologicalComplexIntUpQuasiIsoObjCochainComplexCompSingleFunctorOfNatOfHasExt, PeriodPair.latticeEquiv_symm_apply, HomotopyCategory.instIsTriangulatedIntUpMapHomotopyCategory, Ring.multichoose_neg_of_lt, LaurentSeries.powerSeriesEquivSubring_apply, IsDedekindDomain.HeightOneSpectrum.intValuation_def, DerivedCategory.instEssSurjArrowHomotopyCategoryIntUpMapArrowQh, AddSubmonoid.isLocalizationMap_top_nat_int, FunctionField.inftyValuation.X, HomotopyCategory.quasiIso_eq_subcategoryAcyclic_W, CochainComplex.IsKProjective.leftOrthogonal, FunctionField.inftyValuedFqt.def, HomologicalComplex₂.totalShift₁Iso_trans_totalShift₂Iso, IsDedekindDomain.HeightOneSpectrum.adicValued.uniformContinuousConstSMul, Matrix.map_mul_intCast, RatFunc.valuation_isEquiv_adic_of_not_isEquiv_infty, CochainComplex.isKProjective_iff_leftOrthogonal, DerivedCategory.homologyFunctorFactorsh_hom_app_quotient_obj, LaurentSeries.powerSeriesEquivSubring_coe_apply, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZero_eq, Ring.smeval_ascPochhammer_neg_add, CochainComplex.mappingCone.trianglehMapOfHomotopy_hom₃, LaurentSeries.instLaurentSeriesComplete, Profinite.NobelingProof.GoodProducts.linearIndependentEmpty, IsDedekindDomain.HeightOneSpectrum.valuation_surjective, HomotopyCategory.mem_subcategoryAcyclic_iff, Padic.withValUniformEquiv_cast_apply, CochainComplex.mappingCone.trianglehMapOfHomotopy_hom₁, LaurentSeries.valuation_surjective, LaurentSeries.valuation_coe_ratFunc, HomologicalComplex₂.ι_totalShift₂Iso_inv_f, Padic.coe_withValRingEquiv, AnalyticOnNhd.sum_divisor_le, Padic.comap_mulValuation_eq_int_padicValuation, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_hom_f_f, HomotopyCategory.homologyFunctor_shiftMap_assoc, HomologicalComplex₂.totalShift₂Iso_hom_naturality, HomotopyCategory.distinguished_iff_iso_trianglehOfDegreewiseSplit, LaurentSeries.valuation_compare, Padic.isUniformInducing_cast_withVal, ComplexShape.σ_def, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₃, DerivedCategory.shiftMap_homologyFunctor_map_Q, RatFunc.single_one_eq_pow, CochainComplex.mappingCone.trianglehMapOfHomotopy_hom₂, LaurentSeries.tendsto_valuation, HomotopyCategory.spectralObjectMappingCone_ω₁, CochainComplex.HomComplex.CohomologyClass.equivOfIsKProjective_symm_apply, Profinite.NobelingProof.GoodProducts.span_iff_products, LaurentSeries.coe_range_dense, AddCommGroup.intCast_modEq_intCast, CochainComplex.shiftEval_hom_app, PowerSeries.intValuation_X, IsDedekindDomain.HeightOneSpectrum.adicValued_apply', Ring.smeval_ascPochhammer_succ_neg, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_hom_app_f, Padic.coe_withValRingEquiv_symm, RatFunc.valuation_isEquiv_inftyValuation_of_one_lt_valuation_X, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom_assoc, CochainComplex.mappingCone.mapHomologicalComplexXIso'_hom, IsDedekindDomain.HeightOneSpectrum.adicCompletion_valueGroup_eq, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_inv_f_f, NumberField.HeightOneSpectrum.NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, LaurentSeries.comparePkg_eq_extension, HomotopyCategory.homologyShiftIso_hom_app, instArchimedeanInt, DerivedCategory.Qh_obj_singleFunctors_obj, HomologicalComplex₂.totalShift₁Iso_hom_naturality_assoc, LaurentSeries.valuation_def, CochainComplex.mapBifunctorShift₁Iso_trans_mapBifunctorShift₂Iso, IsDedekindDomain.HeightOneSpectrum.instIsNontrivialWithZeroMultiplicativeIntIntValuation, Profinite.NobelingProof.CC_comp_zero, HomotopyCategory.Pretriangulated.rotate_distinguished_triangle', FunctionField.inftyValuation.C, Profinite.NobelingProof.eval_eq_πJ, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₂, DerivedCategory.instFullFunctorHomotopyCategoryIntUpObjWhiskeringLeftQh, Rat.HeightOneSpectrum.valuation_equiv_padicValuation, Profinite.NobelingProof.CC_exact, LaurentSeries.valuation_le_iff_coeff_lt_log_eq_zero, HomologicalComplex₂.ι_totalShift₂Iso_hom_f, HomologicalComplex₂.instHasTotalIntObjUpShiftFunctor₁, LaurentSeries.uniformContinuous_coeff, Ring.smeval_ascPochhammer_neg_of_lt, Padic.norm_rat_le_one_iff_padicValuation_le_one, CochainComplex.shiftFunctorComm_hom_app_f, Set.integer_valuation_le_one, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletion, Rat.surjective_padicValuation, HomotopyCategory.Pretriangulated.rotate_distinguished_triangle, HomologicalComplex₂.totalShift₁Iso_hom_naturality, HomotopyCategory.quotient_obj_singleFunctors_obj, erdos_ginzburg_ziv_multiset, LaurentSeries.ratfuncAdicComplRingEquiv_apply, Finset.sum_powerset_neg_one_pow_card, Profinite.NobelingProof.injective_πs, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₂, CategoryTheory.Functor.mapCochainComplexShiftIso_hom_app_f, IsDedekindDomain.HeightOneSpectrum.intValuation_exists_uniformizer, CochainComplex.shiftEval_inv_app, DerivedCategory.shiftMap_homologyFunctor_map_Qh, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁, Profinite.NobelingProof.coe_πs', HomotopyCategory.quotient_obj_mem_subcategoryAcyclic_iff_acyclic, natAbs_sum_le, Ico_filter_modEq_eq, Set.integer_eq, Ring.multichoose_neg_add, LaurentPolynomial.isLocalization, Ioc_filter_modEq_eq, ComplexShape.ε_up_ℤ, HomotopyCategory.homologyFunctor_shiftMap, Finset.sum_le_sum_range, CochainComplex.shiftShortComplexFunctorIso_zero_add_hom_app, AddCommGroup.modEq_iff_intModEq, ComplexShape.embeddingDownIntUpInt_f, HomotopyCategory.Pretriangulated.invRotate_distinguished_triangle', padicValuation_le_one, HomologicalComplex₂.D₁_totalShift₂XIso_hom, DerivedCategory.instLinearHomotopyCategoryIntUpQh, GradedObject.eulerChar_eq_sum_finSet_of_finrankSupport_subset, DerivedCategory.homologyFunctorFactorsh_inv_app_quotient_obj_assoc, exists_signed_sum, NumberField.HeightOneSpectrum.toNNReal_valued_eq_adicAbv, NumberField.FinitePlace.norm_embedding', HomotopyCategory.Pretriangulated.isomorphic_distinguished, CochainComplex.mappingConeCompTriangleh_comm₁, HomologicalComplex₂.D₂_totalShift₂XIso_hom, WeierstrassCurve.HasMultiplicativeReduction.badReduction, CochainComplex.HomComplex.CohomologyClass.equivOfIsKProjective_apply, PowerSeries.coe_pow, LaurentSeries.mem_integers_of_powerSeries, LaurentSeries.instIsFractionRingPowerSeries, DerivedCategory.homologyFunctorFactorsh_inv_app_quotient_obj, Valuation.IsRankOneDiscrete.generator_eq_neg_exp_one_of_surjective, CochainComplex.isKInjective_iff_rightOrthogonal, ValuationSubring.algebraMap_injective, CochainComplex.ShiftSequence.shiftIso_inv_app, Profinite.NobelingProof.GoodProducts.linearIndependent_iff_range, CategoryTheory.CommShift₂Setup.int_ε, Function.locallyFinsuppWithin.coe_finsum, Profinite.NobelingProof.GoodProducts.max_eq_eval, meromorphicOrderAt_prod, Valued.exists_pow_lt_of_le_exp_neg_one, IsDedekindDomain.HeightOneSpectrum.valuation_le_one, qExpansion_of_pow, ModularGroup.S_mul_S_eq, instIsPrincipalIdealRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, Ring.smeval_ascPochhammer_self_neg, HomotopyCategory.quotient_obj_mem_subcategoryAcyclic_iff_exactAt, sum_div, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroToFun_eq, ComplexShape.instIsRelIffIntEmbeddingUpIntDownInt, DerivedCategory.isIso_Qh_map_iff, Profinite.NobelingProof.GoodProducts.linearIndependentSingleton, CochainComplex.liftCycles_shift_homologyπ_assoc, FunctionField.inftyValuation_apply, Profinite.NobelingProof.Products.eval_πs_image, Finset.sum_le_sum_Ioc, NumberField.FinitePlace.norm_embedding_int, LaurentSeries.exists_ratFunc_eq_v, HomotopyCategory.mappingConeCompTriangleh_distinguished, CategoryTheory.Functor.mapDerivedCategoryFactorsh_hom_app, Padic.isDenseInducing_cast_withVal, HomologicalComplex.homologyEulerChar_eq_sum_finSet_of_finrankSupport_subset, LaurentSeries.uniformContinuous_withVal_equiv, HomotopyCategory.instIsClosedUnderIsomorphismsIntUpSubcategoryAcyclic, ModEq.sum_zero, CochainComplex.mappingCone.mapHomologicalComplexXIso'_inv, IsDedekindDomain.HeightOneSpectrum.intValuation_apply, LaurentSeries.valuation_X_pow, IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_mem, padicValuation_eq_zero_iff, HomotopyCategory.Pretriangulated.shift_distinguished_triangle, WeierstrassCurve.HasMultiplicativeReduction.multiplicativeReduction, CochainComplex.liftCycles_shift_homologyπ, submodule_toAddSubgroup_index_ne_zero_iff, Rat.padicValuation_le_one_iff, CochainComplex.instAdditiveHomologicalComplexIntUpShiftFunctor, HomologicalComplex₂.ι_totalShift₁Iso_hom_f, ModEq.sum, CategoryTheory.CommShift₂Setup.int_z, Profinite.NobelingProof.GoodProducts.max_eq_eval_unapply, Polynomial.valuation_X_eq_neg_one, Multiset.sum_int_mod, CochainComplex.ShiftSequence.shiftIso_hom_app, instIsOrderedAddMonoid, HomotopyCategory.instCommShiftHomologicalComplexIntUpHomFunctorMapHomotopyCategoryFactors, CochainComplex.mappingCone.map_δ, DerivedCategory.instIsLocalizationHomotopyCategoryIntUpQhTrWSubcategoryAcyclic, DerivedCategory.instHasRightCalculusOfFractionsHomotopyCategoryIntUpQuasiIso
instAddCommSemigroup 📖	CompOp	174 math math: HomotopyCategory.spectralObjectMappingCone_δ'_app, DerivedCategory.instIsLocalizationCochainComplexIntQQuasiIsoUp, CategoryTheory.ShortComplex.ShortExact.instHasSmallLocalizedShiftedHomHomologicalComplexIntUpQuasiIsoX₃CochainComplexMapSingleFunctorOfNatX₁, ComplexShape.embeddingUpIntDownInt_f, CochainComplex.mappingConeCompTriangleh_comm₁_assoc, HomologicalComplex₂.totalShift₂Iso_hom_naturality_assoc, CategoryTheory.InjectiveResolution.ι'_f_zero, HomologicalComplex₂.shiftFunctor₂XXIso_refl, CategoryTheory.Abelian.SpectralObject.coreE₂Cohomological_i₃, CochainComplex.instIsStrictlyLEObjHomologicalComplexIntUpSingle, DerivedCategory.instCommShiftHomologicalComplexIntUpHomFunctorQuotientCompQhIso, CochainComplex.mappingCone.homologySequenceδ_triangleh, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂_assoc, CategoryTheory.Abelian.SpectralObject.instHasSpectralSequenceEIntProdIntCoreE₂Cohomological, CochainComplex.HomComplex.CohomologyClass.equivOfIsKInjective_apply, HomologicalComplex₂.D₂_totalShift₁XIso_hom_assoc, HomologicalComplex₂.D₂_totalShift₂XIso_hom_assoc, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁_assoc, CochainComplex.shiftShortComplexFunctorIso_add'_hom_app, CochainComplex.instIsCompatibleWithShiftHomologicalComplexIntUpQuasiIso, CochainComplex.HomComplex.Cochain.toSingleMk_v, CochainComplex.IsKInjective.rightOrthogonal, CochainComplex.IsKInjective.Qh_map_bijective, HomotopyCategory.instIsHomologicalIntUpHomologyFunctor, DerivedCategory.homologyFunctorFactorsh_hom_app_quotient_obj_assoc, HomologicalComplex₂.ι_totalShift₁Iso_hom_f_assoc, CochainComplex.instIsStrictlyGEObjHomologicalComplexIntUpSingle, HomologicalComplex₂.ι_totalShift₁Iso_inv_f, ComplexShape.eulerCharSignsUpInt_χ, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_eq, DerivedCategory.shiftMap_homologyFunctor_map_Q_assoc, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₁, CochainComplex.HomComplex.CohomologyClass.bijective_toSmallShiftedHom_of_isKProjective, CochainComplex.HomComplex.CohomologyClass.bijective_toSmallShiftedHom_of_isKInjective, CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHom_mk, HomotopyCategory.instAdditiveIntUpShiftFunctor, instIsLocalizationHomologicalComplexIntUpHomotopyCategoryQuotientHomotopyEquivalences, CategoryTheory.Functor.instCommShiftHomotopyCategoryIntUpDerivedCategoryHomMapDerivedCategoryFactorsh, HomologicalComplex₂.ι_totalShift₂Iso_inv_f_assoc, CochainComplex.homologyFunctor_shift, DerivedCategory.instIsTriangulatedHomotopyCategoryIntUpQh, DerivedCategory.shiftMap_homologyFunctor_map_Qh_assoc, HomotopyCategory.Pretriangulated.complete_distinguished_triangle_morphism, HomologicalComplex₂.instHasTotalIntObjUpShiftFunctor₂, HomotopyCategory.mappingCone_triangleh_distinguished, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj_assoc, CochainComplex.HomComplex.Cochain.fromSingleMk_v, HomologicalComplex₂.instHasTotalIntObjUpCompShiftFunctor₁ShiftFunctor₂, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₂, CochainComplex.HomComplex.CohomologyClass.equivOfIsKInjective_symm_apply, instQFactorsThroughHomotopyIntUp, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom, CochainComplex.instLinearHomologicalComplexIntUpShiftFunctor, DerivedCategory.instAdditiveHomotopyCategoryIntUpQh, CategoryTheory.Functor.instCommShiftCochainComplexIntDerivedCategoryHomMapDerivedCategoryFactors, CategoryTheory.ProjectiveResolution.π'_f_zero_assoc, DerivedCategory.instIsLocalizationHomotopyCategoryIntUpQhQuasiIso, HomologicalComplex₂.D₁_totalShift₂XIso_hom_assoc, HomologicalComplex₂.shiftFunctor₁XXIso_refl, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₃, DerivedCategory.instHasLeftCalculusOfFractionsHomotopyCategoryIntUpQuasiIso, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_inv_f_f, CochainComplex.mappingCone.map_inr, CategoryTheory.Functor.mapCochainComplexShiftIso_inv_app_f, HomologicalComplex₂.D₁_totalShift₁XIso_hom_assoc, HomotopyCategory.instLinearIntUpShiftFunctor, CochainComplex.HomComplex.CohomologyClass.equiv_toSmallShiftedHom_mk, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂, HomotopyCategory.Pretriangulated.distinguished_cocone_triangle, HomologicalComplex₂.instHasTotalIntObjUpCompShiftFunctor₂ShiftFunctor₁, HomotopyCategory.instLinearIntUpSingleFunctor, ComplexShape.eulerCharSignsDownInt_χ, HomotopyCategory.instAdditiveIntUpSingleFunctor, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_hom_f_f, HomotopyCategory.Pretriangulated.contractible_distinguished, CategoryTheory.Abelian.SpectralObject.coreE₂Cohomological_i₂, ComplexShape.instIsRelIffIntEmbeddingDownIntUpInt, HomologicalComplex₂.ι_totalShift₁Iso_inv_f_assoc, CategoryTheory.HasExt.hasSmallLocalizedShiftedHom_of_isLE_of_isGE, CategoryTheory.HasExt.instHasSmallLocalizedShiftedHomHomologicalComplexIntUpQuasiIsoOfIsGEOfIsLEOfNat, CochainComplex.IsKProjective.Qh_map_bijective, HomologicalComplex₂.ι_totalShift₂Iso_hom_f_assoc, DerivedCategory.instEssSurjHomotopyCategoryIntUpQh, CategoryTheory.ProjectiveResolution.π'_f_zero, HomotopyCategory.instIsTriangulatedIntUpSubcategoryAcyclic, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_inv_app_f, HomotopyCategory.instIsTriangulatedIntUp, DerivedCategory.instFaithfulFunctorHomotopyCategoryIntUpObjWhiskeringLeftQh, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₃, HomologicalComplex₂.D₁_totalShift₁XIso_hom, HomologicalComplex₂.D₂_totalShift₁XIso_hom, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₁, HomotopyCategory.instIsCompatibleWithShiftHomologicalComplexIntUpHomotopic, CategoryTheory.InjectiveResolution.ι'_f_zero_assoc, CategoryTheory.instHasSmallLocalizedShiftedHomHomologicalComplexIntUpQuasiIsoObjCochainComplexCompSingleFunctorOfNatOfHasExt, HomotopyCategory.instIsTriangulatedIntUpMapHomotopyCategory, DerivedCategory.instEssSurjArrowHomotopyCategoryIntUpMapArrowQh, CategoryTheory.Abelian.SpectralObject.coreE₂Cohomological_deg, HomotopyCategory.quasiIso_eq_subcategoryAcyclic_W, CochainComplex.IsKProjective.leftOrthogonal, HomologicalComplex₂.totalShift₁Iso_trans_totalShift₂Iso, CochainComplex.isKProjective_iff_leftOrthogonal, DerivedCategory.homologyFunctorFactorsh_hom_app_quotient_obj, CochainComplex.mappingCone.trianglehMapOfHomotopy_hom₃, HomotopyCategory.mem_subcategoryAcyclic_iff, CochainComplex.mappingCone.trianglehMapOfHomotopy_hom₁, HomologicalComplex₂.ι_totalShift₂Iso_inv_f, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_hom_f_f, HomotopyCategory.homologyFunctor_shiftMap_assoc, HomologicalComplex₂.totalShift₂Iso_hom_naturality, HomotopyCategory.distinguished_iff_iso_trianglehOfDegreewiseSplit, ComplexShape.σ_def, DerivedCategory.shiftMap_homologyFunctor_map_Q, CochainComplex.mappingCone.trianglehMapOfHomotopy_hom₂, HomotopyCategory.spectralObjectMappingCone_ω₁, CochainComplex.HomComplex.CohomologyClass.equivOfIsKProjective_symm_apply, CochainComplex.shiftEval_hom_app, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_hom_app_f, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom_assoc, CochainComplex.mappingCone.mapHomologicalComplexXIso'_hom, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_inv_f_f, HomotopyCategory.homologyShiftIso_hom_app, DerivedCategory.Qh_obj_singleFunctors_obj, HomologicalComplex₂.totalShift₁Iso_hom_naturality_assoc, HomotopyCategory.Pretriangulated.rotate_distinguished_triangle', CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₂, DerivedCategory.instFullFunctorHomotopyCategoryIntUpObjWhiskeringLeftQh, HomologicalComplex₂.ι_totalShift₂Iso_hom_f, HomologicalComplex₂.instHasTotalIntObjUpShiftFunctor₁, HomotopyCategory.Pretriangulated.rotate_distinguished_triangle, HomologicalComplex₂.totalShift₁Iso_hom_naturality, HomotopyCategory.quotient_obj_singleFunctors_obj, CategoryTheory.Functor.mapCochainComplexShiftIso_hom_app_f, CochainComplex.shiftEval_inv_app, DerivedCategory.shiftMap_homologyFunctor_map_Qh, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁, CategoryTheory.Abelian.SpectralObject.coreE₂Cohomological_i₀, HomotopyCategory.quotient_obj_mem_subcategoryAcyclic_iff_acyclic, Ico_filter_modEq_eq, Ioc_filter_modEq_eq, ComplexShape.ε_up_ℤ, HomotopyCategory.homologyFunctor_shiftMap, CochainComplex.shiftShortComplexFunctorIso_zero_add_hom_app, ComplexShape.embeddingDownIntUpInt_f, HomotopyCategory.Pretriangulated.invRotate_distinguished_triangle', HomologicalComplex₂.D₁_totalShift₂XIso_hom, DerivedCategory.instLinearHomotopyCategoryIntUpQh, DerivedCategory.homologyFunctorFactorsh_inv_app_quotient_obj_assoc, HomotopyCategory.Pretriangulated.isomorphic_distinguished, CochainComplex.mappingConeCompTriangleh_comm₁, HomologicalComplex₂.D₂_totalShift₂XIso_hom, CochainComplex.HomComplex.CohomologyClass.equivOfIsKProjective_apply, DerivedCategory.homologyFunctorFactorsh_inv_app_quotient_obj, CochainComplex.isKInjective_iff_rightOrthogonal, CochainComplex.ShiftSequence.shiftIso_inv_app, HomotopyCategory.quotient_obj_mem_subcategoryAcyclic_iff_exactAt, CategoryTheory.Abelian.SpectralObject.coreE₂Cohomological_i₁, ComplexShape.instIsRelIffIntEmbeddingUpIntDownInt, DerivedCategory.isIso_Qh_map_iff, CochainComplex.liftCycles_shift_homologyπ_assoc, HomotopyCategory.mappingConeCompTriangleh_distinguished, CategoryTheory.Functor.mapDerivedCategoryFactorsh_hom_app, HomotopyCategory.instIsClosedUnderIsomorphismsIntUpSubcategoryAcyclic, CochainComplex.mappingCone.mapHomologicalComplexXIso'_inv, HomotopyCategory.Pretriangulated.shift_distinguished_triangle, CochainComplex.liftCycles_shift_homologyπ, CochainComplex.instAdditiveHomologicalComplexIntUpShiftFunctor, HomologicalComplex₂.ι_totalShift₁Iso_hom_f, CochainComplex.ShiftSequence.shiftIso_hom_app, HomotopyCategory.instCommShiftHomologicalComplexIntUpHomFunctorMapHomotopyCategoryFactors, CochainComplex.mappingCone.map_δ, DerivedCategory.instIsLocalizationHomotopyCategoryIntUpQhTrWSubcategoryAcyclic, DerivedCategory.instHasRightCalculusOfFractionsHomotopyCategoryIntUpQuasiIso
instAddGroup 📖	CompOp	835 math math: ValueDistribution.logCounting_zero, HomotopyCategory.spectralObjectMappingCone_δ'_app, CategoryTheory.InjectiveResolution.Hom.hom'_f, zmultiples_natAbs, DerivedCategory.instIsLocalizationCochainComplexIntQQuasiIsoUp, CochainComplex.acyclic_op, CategoryTheory.ShortComplex.ShortExact.instHasSmallLocalizedShiftedHomHomologicalComplexIntUpQuasiIsoX₃CochainComplexMapSingleFunctorOfNatX₁, CochainComplex.triangleOfDegreewiseSplit_obj₁, emod_lt_abs, CochainComplex.mappingConeCompTriangleh_comm₁_assoc, CochainComplex.HomComplex.Cochain.rightShiftAddEquiv_symm_apply, CochainComplex.HomComplex.Cochain.fromSingleMk_neg, CochainComplex.mappingCone.δ_inl, CochainComplex.mappingCone.inl_v_descCochain_v_assoc, zmultiples_one, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_neg, CochainComplex.mappingCocone.inr_v_snd_v_assoc, abs_le_sqrt, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_add, DerivedCategory.right_fac, CochainComplex.HomComplex.Cocycle.fromSingleMk_add, CochainComplex.mappingCone.ofHom_desc, negOnePow_abs, CochainComplex.HomComplex.Cocycle.leftShiftAddEquiv_symm_apply, CochainComplex.mappingCone.inr_f_d_assoc, CochainComplex.quasiIsoAt_πTruncGE, CochainComplex.mappingCocone.inl_v_descCochain_v, CochainComplex.HomComplex.Cochain.δ_single, CochainComplex.mappingConeCompTriangle_obj₂, norm_jacobiTheta₂_term_le, CochainComplex.Lifting.π_f_cochain₁_v_ι_f, CochainComplex.HomComplex.Cocycle.equivHom_symm_apply, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₃, CochainComplex.isStrictlyGE_shift, norm_jacobiTheta₂_term_fderiv_ge, CochainComplex.mappingCone.id, CochainComplex.shiftFunctorZero_eq, CategoryTheory.InjectiveResolution.ι'_f_zero, CochainComplex.mappingCone.liftCochain_v_snd_v_assoc, CochainComplex.mappingCone.inr_f_fst_v, CochainComplex.isStrictlyLE_iff, cast_abs, CochainComplex.HomComplex.Cochain.leftShift_smul, CochainComplex.mappingCone.inr_desc_assoc, CochainComplex.mappingCocone.inr_v_snd_v, CochainComplex.HomComplex.Cochain.fromSingleEquiv_fromSingleMk, CochainComplex.quasiIso_truncLEMap_iff, addLeft_one_isCycle, Zsqrtd.abs_norm, CochainComplex.mappingCone.triangle_mor₁, CategoryTheory.Abelian.SpectralObject.coreE₂Cohomological_i₃, CochainComplex.IsKInjective.nonempty_homotopy_zero, CochainComplex.mappingCone.liftCochain_v_snd_v, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₂, ComplexShape.instIsTruncLENatIntEmbeddingUpIntLE, CochainComplex.Lifting.comp_coe_cocyle₁'_v_eq_zero, RootPairing.Base.cartanMatrix_map_abs, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₃, CochainComplex.exactAt_op, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_postcomp, ComplexShape.instIsRelIffNatIntEmbeddingUpIntLE, CochainComplex.homologyMap_homologyδOfTriangle_assoc, EisensteinSeries.abs_le_right_of_norm, CochainComplex.mappingCone.homologySequenceδ_triangleh, CochainComplex.HomComplex.Cocycle.fromSingleMk_surjective, CochainComplex.instLinearIntFunctorSingleFunctors, abs_sub_lt_of_lt_lt, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂_assoc, CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₃, CochainComplex.IsKProjective.homotopyZero_def, CategoryTheory.Abelian.SpectralObject.instHasSpectralSequenceEIntProdIntCoreE₂Cohomological, NumberField.abs_discr_ge', CochainComplex.mappingCone.d_snd_v, CochainComplex.HomComplex.Cochain.rightUnshift_neg, CochainComplex.HomComplex.Cochain.δ_fromSingleMk, FractionalIdeal.absNorm_eq', NumberField.abs_discr_ge, CochainComplex.HomComplex.Cochain.map_v, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_flip_hom_app, CochainComplex.ConnectData.map_comp_map, CochainComplex.HomComplex.leftHomologyData_K_coe, CochainComplex.mappingConeCompTriangle_mor₃, CochainComplex.HomComplex.Cochain.shift_add, CochainComplex.HomComplex.Cochain.comp_id, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_add, CochainComplex.Plus.mono_iff, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_sub, CategoryTheory.ProjectiveResolution.cochainComplex_d, CochainComplex.HomComplex.Cochain.toSingleMk_neg, CochainComplex.HomComplex.Cochain.ofHom_v_comp_d, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₂_assoc, CochainComplex.instQuasiIsoAtIntπTruncGE, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁_assoc, CochainComplex.shiftShortComplexFunctorIso_add'_hom_app, CochainComplex.HomComplex.Cochain.map_zero, CochainComplex.cm5b.fac, DerivedCategory.singleFunctorsPostcompQIso_inv_hom, CochainComplex.HomComplex.Cochain.toSingleMk_v, CochainComplex.HomComplex.leftHomologyData'_i, CochainComplex.ConnectData.cochainComplex_X, ComplexShape.instHasNoLoopIntDown, ComplexShape.Embedding.embeddingUpInt_areComplementary, CochainComplex.HomComplex.Cochain.leftShiftLinearEquiv_apply, CochainComplex.HomComplex.Cochain.shift_neg, range_castAddHom, DerivedCategory.subsingleton_hom_of_isStrictlyLE_of_isStrictlyGE, CochainComplex.instIsIsoIntπTruncGEOfIsStrictlyGE, DerivedCategory.homologyFunctorFactorsh_hom_app_quotient_obj_assoc, DerivedCategory.homologyFunctorFactors_hom_naturality, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f_assoc, CochainComplex.homotopyUnop_hom_eq, CochainComplex.HomComplex.Cochain.toSingleMk_add, HomologicalComplex₂.ι_totalShift₁Iso_hom_f_assoc, CochainComplex.mappingCone.inr_f_d, CochainComplex.mappingCocone.lift_fst, CochainComplex.HomComplex.δ_v, CochainComplex.HomComplex.Cochain.comp_v, AbsoluteValue.exists_partition_int, CochainComplex.HomComplex.Cochain.comp_zero_cochain_v, NumberField.house_intCast, CochainComplex.mappingCone.inr_f_descShortComplex_f_assoc, CochainComplex.HomComplex.Cochain.neg_v, CochainComplex.HomComplex.Cocycle.equivHomShift'_symm_apply, ValueDistribution.logCounting_top, CochainComplex.HomComplex.Cochain.sub_v, mabs_zpow, CochainComplex.mappingCone.liftCochain_v_descCochain_v, CochainComplex.mappingCone.lift_f_fst_v, CochainComplex.mappingCone.inl_v_triangle_mor₃_f, CochainComplex.XIsoOfEq_shift, HomologicalComplex₂.ι_totalShift₁Iso_inv_f, CochainComplex.mappingCocone.liftCochain_v_snd_v_assoc, CochainComplex.ιTruncLE_naturality_assoc, CochainComplex.Lifting.exists_hom, CochainComplex.HomComplex.Cochain.rightUnshift_comp, CochainComplex.HomComplex.Cochain.rightUnshift_units_smul, CochainComplex.mappingCone.inr_triangleδ, CochainComplex.HomComplex.Cochain.ofHoms_comp, DerivedCategory.shiftMap_homologyFunctor_map_Q_assoc, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_sub, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₁, CochainComplex.HomComplex.leftHomologyData_π_hom_apply, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_sub, CochainComplex.instIsStrictlyLEExtendNatIntEmbeddingDownNatOfNat, CochainComplex.homologyFunctorFactors_hom_app_homologyδOfTriangle_assoc, CochainComplex.πTruncGE_naturality, CochainComplex.mappingCone.id_X, DerivedCategory.triangleOfSES_mor₁, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CochainComplex.HomComplex.Cochain.single_zero, CochainComplex.mappingCocone.inr_v_desc_f_assoc, CochainComplex.mappingCone.inr_descShortComplex_assoc, DerivedCategory.mappingCone_triangle_distinguished, subgroup_cyclic, LaurentPolynomial.antipode_T, CochainComplex.mappingConeCompHomotopyEquiv_comm₂_assoc, CochainComplex.homologyδOfTriangle_homologyMap_assoc, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_sub, CochainComplex.mappingConeCompHomotopyEquiv_hom_inv_id, Rat.num_abs_eq_abs_num, CochainComplex.HomComplex.leftHomologyData_i_hom_apply, CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHom_mk, CochainComplex.HomComplex.Cochain.fromSingleMk_postcomp, CochainComplex.mappingCone.d_snd_v'_assoc, CochainComplex.HomComplex.Cochain.shift_zero, Subgroup.range_zpowersHom, MeromorphicOn.divisor_inv, CochainComplex.shiftFunctorZero_inv_app_f, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_zero, HomologicalComplex₂.ι_totalShift₂Iso_inv_f_assoc, CochainComplex.instQuasiIsoAtIntιTruncLE, CochainComplex.HomComplex.Cochain.leftShift_comp, CategoryTheory.ProjectiveResolution.extAddEquivCohomologyClass_symm_apply, CochainComplex.triangleOfDegreewiseSplit_obj₂, CochainComplex.mappingCocone.triangle_obj₂, CochainComplex.HomComplex.Cochain.zero_cochain_comp_v, CochainComplex.MappingConeCompHomotopyEquiv.hom_inv_id_assoc, CochainComplex.g_shortComplexTruncLEX₃ToTruncGE, CochainComplex.quasiIsoAt_ιTruncLE, CategoryTheory.Functor.mapCochainComplexPlus_obj_obj_X, CochainComplex.homologyδOfTriangle_homologyMap, CochainComplex.HomComplex.Cochain.toSingleMk_v_eq_zero, CochainComplex.isKInjective_shift_iff, CochainComplex.isStrictlyGE_iff, CochainComplex.homologyMap_comp_eq_zero_of_distTriang, cast_natAbs, CochainComplex.HomComplex.Cochain.leftShift_rightShift_eq_negOnePow_rightShift_leftShift, CochainComplex.mappingCone.lift_f_fst_v_assoc, CochainComplex.HomComplex.Cocycle.toSingleMk_surjective, CochainComplex.mappingCocone.id_X, Equiv.Perm.sign_abs, DerivedCategory.to_singleFunctor_obj_eq_zero_of_injective, DerivedCategory.right_fac_of_isStrictlyLE_of_isStrictlyGE, instIsAddCyclicInt, CochainComplex.mappingCocone.triangle_obj₃, CochainComplex.HomComplex.Cochain.leftShift_rightShift, DerivedCategory.instIsIsoMapCochainComplexIntQOfQuasiIso, ComplexShape.embeddingUpNat_f, CochainComplex.HomComplex.Cochain.ofHom_neg, CochainComplex.isSplitEpi_to_singleFunctor_obj_of_projective, CochainComplex.HomComplex.Cocycle.toSingleMk_add, DerivedCategory.triangleOfSES_obj₃, CochainComplex.HomComplex.Cochain.zero_v, CochainComplex.homologyMap_exact₃_of_distTriang, DerivedCategory.instLinearCochainComplexIntQ, CochainComplex.homologyMap_exact₂_of_distTriang, ComplexShape.instIsTruncGENatIntEmbeddingUpIntGE, CochainComplex.isZero_of_isStrictlyLE, addSubgroup_index_ne_zero_iff, one_le_abs, dist_eq', CochainComplex.instAdditiveIntFunctorSingleFunctors, CochainComplex.shiftFunctor_obj_X, CochainComplex.mappingConeCompHomotopyEquiv_comm₁, CochainComplex.mappingCone.triangleMap_hom₂, Ioo_eq_finset_map, CochainComplex.mappingCocone.liftCochain_v_fst_f, Mathlib.Tactic.Ring.smul_int, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₂, abs_le_sqrt_iff_sq_le, CochainComplex.HomComplex.Cocycle.toSingleMk_mem_coboundaries_iff, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₂, CochainComplex.HomComplex.Cochain.map_add, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj_assoc, CategoryTheory.ProjectiveResolution.extMk_hom, CochainComplex.mappingCone.triangleRotateShortComplex_X₂, CochainComplex.HomComplex.Cochain.fromSingleMk_v, CochainComplex.HomComplex.Cochain.fromSingleMk_add, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_neg, Nat.cast_natAbs, CochainComplex.HomComplex.Cochain.shift_smul, CochainComplex.homologyMap_exact₁_of_distTriang, CochainComplex.HomComplex.Cochain.leftShiftAddEquiv_apply, CochainComplex.HomComplex.Cochain.ofHomotopy_refl, CategoryTheory.ProjectiveResolution.Hom.hom'_f_assoc, CochainComplex.IsKInjective.homotopyZero_def, CochainComplex.mappingCone.ext_from_iff, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₁, CochainComplex.mappingCocone.triangle_mor₁, CochainComplex.HomComplex.Cocycle.toSingleMk_zero, CochainComplex.HomComplex.Cochain.rightShiftAddEquiv_apply, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv, CochainComplex.isIso_πTruncGE_iff, CochainComplex.HomComplex.Cochain.leftUnshift_v, FixedDetMatrices.reps_entries_le_m', CochainComplex.Plus.instHasFiniteLimits, NumberField.abs_discr_gt_two, CochainComplex.mappingConeCompHomotopyEquiv_comm₁_assoc, CochainComplex.Plus.instHasTwoOutOfThreePropertyQuasiIso, CochainComplex.ConnectData.map_f, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₂, HurwitzZeta.hasSum_int_cosZeta, AddSubgroup.range_zmultiplesHom, norm_abs_zsmul, MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_right, CochainComplex.mappingCone.triangleRotateShortComplex_X₃, zmultiplesHom_ker_eq, CochainComplex.HomComplex.Cochain.rightShift_leftShift, DerivedCategory.triangleOfSES.map_hom₁, NumberField.rootDiscr_def, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, CochainComplex.HomComplex.Cochain.ofHom_v, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom, CategoryTheory.Functor.mapCochainComplexPlusCompι_inv_app_f, CochainComplex.HomComplex.Cochain.ofHom_sub, CochainComplex.HomComplex.Cochain.leftUnshift_smul, norm_zpow_abs, CochainComplex.mappingCone.inr_f_snd_v, CochainComplex.instIsKInjectiveObjIntShiftFunctor, CochainComplex.mappingConeCompTriangle_mor₃_naturality, CategoryTheory.Functor.instCommShiftCochainComplexIntDerivedCategoryHomMapDerivedCategoryFactors, CochainComplex.instIsClosedUnderIsomorphismsIntPlus, CochainComplex.HomComplex.Cochain.shiftLinearMap_apply, Submodule.span_singleton_toAddSubgroup_eq_zmultiples, CategoryTheory.ProjectiveResolution.π'_f_zero_assoc, ZMod.intCast_abs_mod_two, CochainComplex.HomComplex.Cocycle.toSingleMk_coe, CochainComplex.mappingCone.triangleRotateShortComplex_X₁, CochainComplex.Plus.modelCategoryQuillen.cm5a_cof.step, MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_left, DerivedCategory.left_fac_of_isStrictlyLE_of_isStrictlyGE, CochainComplex.shiftFunctor_map_f', CochainComplex.mappingCone.ext_to_iff, CochainComplex.ConnectData.restrictionLEIso_inv_f, CochainComplex.mappingCone.inr_f_desc_f, CategoryTheory.ProjectiveResolution.Hom.hom'_comp_π', CochainComplex.HomComplex.Cochain.rightShift_zero, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₃, CategoryTheory.ProjectiveResolution.Hom.hom'_f, CochainComplex.singleFunctor_obj_d, CochainComplex.quasiIso_truncGEMap_iff, CochainComplex.Plus.instIsClosedUnderLimitsOfShapeIntPlusOfFinCategoryOfHasLimitsOfShape, CochainComplex.quasiIso_shift_iff, CochainComplex.HomComplex.Cochain.rightUnshift_v, HomotopyCategory.composableArrowsFunctor_obj, ComplexShape.instIsRelIffNatIntEmbeddingDownNat, CochainComplex.mappingCone.inl_v_desc_f_assoc, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₂, CochainComplex.shiftFunctorAdd'_inv_app_f', CochainComplex.exactAt_of_isLE, abs_le_one_iff, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_inv_f_f, EisensteinSeries.finGcdMap_smul, norm_intCast_abs, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_zero, CochainComplex.mappingCone.map_inr, CategoryTheory.Functor.mapCochainComplexShiftIso_inv_app_f, CochainComplex.shiftFunctorAdd'_eq, CochainComplex.shiftFunctorAdd'_inv_app_f, CochainComplex.mappingCone.liftCochain_v_fst_v, CochainComplex.HomComplex.CohomologyClass.equiv_toSmallShiftedHom_mk, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂, MeromorphicOn.divisor_fun_zpow, CochainComplex.HomComplex.Cochain.fromSingleMk_zero, CochainComplex.mappingCone.decomp_from, CochainComplex.mappingCone.inl_v_triangle_mor₃_f_assoc, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₁, CochainComplex.mappingConeCompTriangle_mor₁, CochainComplex.mappingCone.inr_triangleδ_assoc, CochainComplex.cm5b.instIsStrictlyGEBiprodIntMappingConeIdIOfHAddOfNat, CochainComplex.HomComplex.Cochain.leftShift_zero, CochainComplex.mappingCone.inl_v_snd_v_assoc, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_zero, CategoryTheory.ProjectiveResolution.Hom.hom'_comp_π'_assoc, Icc_eq_finset_map, CochainComplex.instLinearIntShiftFunctor, CochainComplex.triangleOfDegreewiseSplit_mor₂, absNorm_under_mem, CochainComplex.HomComplex.Cochain.ofHoms_v_comp_d, CochainComplex.mappingCone.inr_f_triangle_mor₃_f, CochainComplex.HomComplex.Cocycle.fromSingleMk_coe, DerivedCategory.isLE_Q_obj_iff, CochainComplex.cm5b.fac_assoc, MeromorphicOn.divisor_zpow, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_hom_f_f, CochainComplex.IsKProjective.nonempty_homotopy_zero, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_inv, CochainComplex.triangleOfDegreewiseSplit_obj₃, RootPairing.Base.height_add_zsmul, nnnorm_intCast_abs, CochainComplex.shiftFunctorZero'_hom_app_f, mem_zmultiples_iff, CategoryTheory.Functor.mapCochainComplexPlusCompι_hom_app_f, DerivedCategory.triangleOfSES_obj₁, range_nsmulAddMonoidHom, CategoryTheory.Abelian.SpectralObject.coreE₂Cohomological_i₂, FractionalIdeal.absNorm_eq, CochainComplex.HomComplex.Cochain.fromSingleMk_surjective, ComplexShape.instIsRelIffNatIntEmbeddingUpIntGE, nnnorm_zpow_abs, CochainComplex.mappingCone.triangle_mor₂, HomologicalComplex₂.ι_totalShift₁Iso_inv_f_assoc, natAbs_abs, CochainComplex.HomComplex.Cocycle.leftUnshift_coe, CochainComplex.HomComplex.Cochain.equivHomotopy_apply_of_eq, Ioc_eq_finset_map, CochainComplex.MappingConeCompHomotopyEquiv.hom_inv_id, CochainComplex.mappingCone.d_snd_v_assoc, CochainComplex.instAdditiveIntShiftFunctor, zpow_abs_eq_one, CochainComplex.shiftFunctor_map_f, CochainComplex.quasiIsoAt_shift_iff, CochainComplex.mappingCone.d_snd_v', CochainComplex.HomComplex.Cocycle.equivHomShift_symm_apply, CochainComplex.instIsKProjectiveObjIntShiftFunctor, CochainComplex.mappingCocone.inl_v_snd_v, CochainComplex.HomComplex.Cochain.rightShift_smul, CochainComplex.HomComplex.Cochain.map_comp, CochainComplex.mappingCocone.triangle_mor₂, CochainComplex.mappingCocone.lift_f_snd_v_assoc, CochainComplex.homotopyOp_hom_eq, CochainComplex.mappingCone.inr_f_descCochain_v_assoc, CochainComplex.HomComplex.Cochain.map_sub, CochainComplex.HomComplex.Cocycle.homOf_f, CochainComplex.instQuasiIsoIntιTruncLEOfIsLE, CochainComplex.IsKProjective.Qh_map_bijective, CochainComplex.mappingCone.d_fst_v_assoc, CochainComplex.homOfDegreewiseSplit_f, CochainComplex.shiftFunctorAdd_inv_app_f, CochainComplex.HomComplex.Cochain.toSingleMk_surjective, ComplexShape.boundaryGE_embeddingUpIntGE_iff, DerivedCategory.isGE_Q_obj_iff, HomologicalComplex₂.ι_totalShift₂Iso_hom_f_assoc, CochainComplex.mappingCone.map_id, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₁, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₂, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_inv_app, CochainComplex.mappingCocone.liftCochain_v_fst_f_assoc, CochainComplex.mappingConeCompTriangle_obj₃, CategoryTheory.ProjectiveResolution.π'_f_zero, CochainComplex.mappingCone.inl_v_fst_v, addRight_one_isCycle, CochainComplex.isLE_iff, CochainComplex.ConnectData.cochainComplex_d, abs_negOnePow, isUnit_iff_abs_eq, CochainComplex.HomComplex.Cocycle.fromSingleMk_neg, CochainComplex.Lifting.π_f_cochain₁_v_ι_f_assoc, abs_sign_of_ne_zero, sign_eq_abs_ediv, CochainComplex.exists_iso_single, CochainComplex.HomComplex.Cocycle.rightShiftAddEquiv_symm_apply, CochainComplex.HomComplex.Cochain.shift_units_smul, CochainComplex.ConnectData.restrictionLEIso_hom_f, ofAdd_mul, CochainComplex.mappingCone.inr_desc, Profinite.NobelingProof.GoodProducts.finsuppSum_mem_span_eval, CochainComplex.exactAt_of_isGE, CochainComplex.shiftFunctorAdd_eq, CochainComplex.HomComplex.Cochain.leftShiftLinearEquiv_symm_apply, CochainComplex.mappingCone.inr_f_descCochain_v, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f, CochainComplex.cm5b.instQuasiIsoIntP, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₃, ZLattice.exists_forall_abs_repr_le_norm, CochainComplex.mappingCocone.lift_f_fst_f, CochainComplex.mappingCocone.inr_v_fst_f_assoc, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₂_assoc, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₁, CochainComplex.mappingCone.isZero_X_iff, CochainComplex.mappingCone.quasiIso_descShortComplex, uIcc_eq_finset_map, Ideal.span_singleton_toAddSubgroup_eq_zmultiples, NumberField.finite_of_discr_bdd, DerivedCategory.instIsGEObjCochainComplexIntQOfIsGE, CochainComplex.mappingConeCompHomotopyEquiv_comm₂, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_hom_assoc, CochainComplex.mappingCocone.lift_f_snd_v, CochainComplex.mappingCocone.lift_fst_assoc, CochainComplex.quasiIso_πTruncGE_iff, CochainComplex.HomComplex.δ_zero_cochain_v, CochainComplex.HomComplex.Cochain.units_smul_v, CochainComplex.HomComplex.Cochain.δ_toSingleMk, CochainComplex.cm5b.instMonoFIntI, CochainComplex.HomComplex.CohomologyClass.toHom_bijective, CochainComplex.HomComplex.Cochain.fromSingleMk_precomp, CochainComplex.HomComplex.Cochain.leftUnshift_add, CochainComplex.isGE_iff, MeromorphicOn.divisor_fun_inv, CochainComplex.mappingCocone.liftCochain_v_snd_v, CochainComplex.HomComplex.Cocycle.fromSingleMk_zero, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃_assoc, CochainComplex.instIsIsoIntιTruncLEOfIsStrictlyLE, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_hom, absNorm_under_dvd_absNorm, CochainComplex.mappingCone.inr_f_fst_v_assoc, CategoryTheory.ProjectiveResolution.instProjectiveXIntCochainComplex, CategoryTheory.InjectiveResolution.ι'_f_zero_assoc, CochainComplex.mappingCone.inl_v_d_assoc, CochainComplex.shiftFunctorZero'_inv_app_f, CochainComplex.mappingCone.inl_v_desc_f, CochainComplex.mappingCone.cocycleOfDegreewiseSplit_triangleRotateShortComplexSplitting_v, CochainComplex.HomComplex.Cochain.rightShift_units_smul, CochainComplex.isZero_of_isStrictlyGE, CategoryTheory.instHasSmallLocalizedShiftedHomHomologicalComplexIntUpQuasiIsoObjCochainComplexCompSingleFunctorOfNatOfHasExt, DerivedCategory.exists_iso_Q_obj_of_isGE_of_isLE, DerivedCategory.triangleOfSES.map_hom₃, CochainComplex.HomComplex.Cochain.rightUnshift_smul, HomotopyCategory.composableArrowsFunctor_map, CochainComplex.mappingCone.map_comp_assoc, CochainComplex.HomComplex.Cocycle.equivHomShift'_apply, CochainComplex.instQuasiIsoIntMapHomologicalComplexUpShiftFunctor, CategoryTheory.InjectiveResolution.Hom.ι'_comp_hom'_assoc, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃_assoc, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_add, emod_abs, CategoryTheory.Abelian.SpectralObject.coreE₂Cohomological_deg, CochainComplex.HomComplex.Cochain.smul_v, CochainComplex.isSplitMono_from_singleFunctor_obj_of_injective, CochainComplex.mappingCone.triangleRotateShortComplexSplitting_r, addSubgroupClosure_one, CategoryTheory.InjectiveResolution.Hom.hom'_f_assoc, abs_eq_normalize, ArithmeticFunction.abs_moebius_eq_one_of_squarefree, CochainComplex.HomComplex.Cochain.δ_shift, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₃, CochainComplex.HomComplex.Cochain.fromSingleMk_sub, CochainComplex.mappingCone.inl_v_descShortComplex_f_assoc, CFC.abs_intCast, DerivedCategory.from_singleFunctor_obj_eq_zero_of_projective, CochainComplex.Plus.instHasFiniteColimits, HomologicalComplex₂.totalShift₁Iso_trans_totalShift₂Iso, DerivedCategory.exists_iso_Q_obj_of_isGE, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_flip_inv_app, CochainComplex.cm5b.instInjectiveXIntI, ZLattice.abs_repr_lt_of_norm_lt, CochainComplex.cm5b.instMonoIntI, CategoryTheory.ProjectiveResolution.extAddEquivCohomologyClass_apply, sign_mul_self_eq_abs, CochainComplex.mappingCocone.inl_v_fst_f_assoc, norm_jacobiTheta₂'_term_le, ComplexShape.instIsRelIffNatIntEmbeddingUpNat, CochainComplex.HomComplex.Cocycle.toSingleMk_sub, ZMod.ker_intCastAddHom, CochainComplex.mappingCone.map_comp, DerivedCategory.homologyFunctorFactorsh_hom_app_quotient_obj, CategoryTheory.InjectiveResolution.extMk_hom, CategoryTheory.InjectiveResolution.cochainComplex_d_assoc, toAdd_zpow, CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₁, CochainComplex.HomComplex.Cocycle.fromSingleMk_sub, CochainComplex.shortComplexTruncLE_shortExact, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_zero, CochainComplex.Plus.instIsClosedUnderColimitsOfShapeIntPlusOfFinCategoryOfHasColimitsOfShape, CochainComplex.quasiIso_ιTruncLE_iff, CochainComplex.cm5b.i_f_comp, CochainComplex.HomComplex.Cochain.δ_rightUnshift, CochainComplex.mappingCone.inr_snd, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_neg, CochainComplex.mappingCone.decomp_to, CochainComplex.HomComplex.leftHomologyData_H_coe, CochainComplex.HomComplex.leftHomologyData'_K_coe, CochainComplex.HomComplex.Cochain.leftUnshift_units_smul, CochainComplex.mappingCone.inl_fst, CochainComplex.HomComplex.Cochain.rightShiftLinearEquiv_apply, CochainComplex.HomComplex.Cocycle.shift_coe, index_zmultiples, ComplexShape.embeddingUpIntLE_f, CochainComplex.mappingCone.liftCochain_v_fst_v_assoc, CochainComplex.mappingCone.lift_desc_f, CochainComplex.isStrictlyLE_shift, ModularGroup.abs_c_le_one, CochainComplex.ConnectData.restrictionGEIso_inv_f, CochainComplex.instFullIntSingleFunctor, Function.locallyFinsuppWithin.restrict_posPart, CochainComplex.HomComplex.Cochain.δ_rightShift, DerivedCategory.right_fac_of_isStrictlyLE, HomologicalComplex₂.ι_totalShift₂Iso_inv_f, CochainComplex.ConnectData.map_id, CochainComplex.HomComplex.Cochain.leftShift_v, CochainComplex.mappingCone.desc_f, CochainComplex.mappingCone.d_fst_v'_assoc, CochainComplex.mappingCocone.inr_v_fst_f, CochainComplex.HomComplex.Cochain.rightUnshift_add, CochainComplex.HomComplex.Cochain.toSingleMk_zero, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_hom_f_f, MeromorphicOn.negPart_divisor_add_le_max, ComplexShape.embeddingDownNat_f, HomotopyCategory.homologyFunctor_shiftMap_assoc, CochainComplex.mappingCone.inl_v_d, CochainComplex.isZero_of_isGE, CochainComplex.shiftFunctor_obj_X', HomotopyCategory.distinguished_iff_iso_trianglehOfDegreewiseSplit, CochainComplex.HomComplex.Cochain.shift_v, CochainComplex.shiftFunctorZero_hom_app_f, zsmul_eq_mul, DerivedCategory.shiftMap_homologyFunctor_map_Q, CochainComplex.mappingCone.inr_f_snd_v_assoc, Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_symm_apply, sign_eq_ediv_abs', CochainComplex.triangleOfDegreewiseSplit_mor₃, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv_assoc, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_extMk, CochainComplex.HomComplex.Cochain.shiftAddHom_apply, subgroup_index_ne_zero_iff, CategoryTheory.InjectiveResolution.instQuasiIsoIntι', CochainComplex.HomComplex.Cochain.δ_leftUnshift, NumberField.abs_discr_ge_of_isTotallyComplex, HomotopyCategory.spectralObjectMappingCone_ω₁, CochainComplex.HomComplex.Cocycle.toSingleMk_neg, LaurentPolynomial.antipode_C, CochainComplex.mappingCone.d_fst_v', CochainComplex.shiftFunctorAdd'_hom_app_f', CochainComplex.mappingCone.inl_v_descCochain_v, CochainComplex.HomComplex.Cochain.leftShift_add, CochainComplex.HomComplex.Cochain.leftShift_comp_zero_cochain, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₃_assoc, CochainComplex.shiftEval_hom_app, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃, CochainComplex.Lifting.hasLift, CochainComplex.instHasMapBifunctorObjIntShiftFunctor_1, abs_le_floor_nnreal_iff, CochainComplex.HomComplex.Cocycle.equivHomShift_comp, Ico_eq_finset_map, CochainComplex.cm5b.i_f_comp_assoc, EisensteinSeries.abs_le_left_of_norm, CochainComplex.HomComplex_X, CochainComplex.instIsStrictlyGEExtendNatIntEmbeddingUpNatOfNat, CochainComplex.ConnectData.homologyMap_map_of_eq_succ, CochainComplex.HomComplex.leftHomologyData'_H_coe, RootPairing.GeckConstruction.lie_e_lie_f_apply, CochainComplex.mappingCone.triangleRotateShortComplex_g, CochainComplex.shiftFunctor_obj_d', CochainComplex.instHasMapBifunctorObjIntShiftFunctor, CochainComplex.ιTruncLE_naturality, ZMod.abs_valMinAbs_eq_abs_valMinAbs, AddGroup.instFGInt, norm_intCast_eq_abs_mul_norm_one, CochainComplex.HomComplex.Cocycle.equivHom_apply, modEq_abs, CochainComplex.mappingCone.inr_descShortComplex, DerivedCategory.instAdditiveCochainComplexIntQ, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom_assoc, CochainComplex.HomComplex.Cocycle.fromSingleMk_precomp, CochainComplex.ι_mapBifunctorShift₁Iso_hom_f_assoc, HurwitzZeta.hasSum_int_sinZeta, CochainComplex.cm5b.I_d, CochainComplex.triangleOfDegreewiseSplit_mor₁, CochainComplex.mappingCone.mapHomologicalComplexXIso'_hom, abs_ediv_le_abs, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_inv_f_f, CochainComplex.HomComplex.Cochain.d_comp_ofHom_v, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₃, CochainComplex.HomComplex.Cochain.leftShift_units_smul, CochainComplex.HomComplex.Cochain.equivHomotopy_apply_coe, HomotopyCategory.homologyShiftIso_hom_app, CochainComplex.shiftFunctorAdd_hom_app_f, ComplexShape.instIsTruncLENatIntEmbeddingDownNat, FractionalIdeal.absNorm_div_norm_eq_absNorm_div_norm, CochainComplex.HomComplex.δ_map, CochainComplex.mapBifunctorShift₁Iso_trans_mapBifunctorShift₂Iso, CochainComplex.mappingCone.inl_v_descShortComplex_f, abs_lt_one_iff, CochainComplex.mappingCocone.triangle_obj₁, CochainComplex.isIso_ιTruncLE_iff, CochainComplex.HomComplex.Cochain.d_comp_ofHoms_v, CochainComplex.HomComplex.Cochain.toSingleMk_postcomp, CochainComplex.HomComplex.Cochain.ofHom_add, CochainComplex.mappingCone.triangleRotateShortComplexSplitting_s, le_abs_of_dvd, CochainComplex.mappingCone.inr_f_descShortComplex_f, ZLattice.normBound_spec, CochainComplex.mappingCone.map_descShortComplex, DerivedCategory.triangleOfSES.map_hom₂, CochainComplex.HomComplex.Cochain.id_comp, CochainComplex.mappingCocone.inl_v_desc_f, zsmul_int_int, CategoryTheory.ProjectiveResolution.instQuasiIsoIntπ', CochainComplex.HomComplex.Cochain.single_v_eq_zero', DerivedCategory.exists_iso_Q_obj_of_isLE, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₂, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₃, CochainComplex.shiftFunctorAdd'_hom_app_f, CochainComplex.HomComplex.Cochain.ofHom_zero, CochainComplex.g_shortComplexTruncLEX₃ToTruncGE_assoc, CochainComplex.mappingCone.inr_f_triangle_mor₃_f_assoc, CochainComplex.HomComplex.leftHomologyData'_π, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_add, NumberField.abs_discr_rpow_ge_of_isTotallyComplex, CochainComplex.mappingCone.triangleMap_hom₁, MeromorphicOn.negPart_divisor_add_le_add, HomologicalComplex₂.ι_totalShift₂Iso_hom_f, Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply, nnnorm_abs_zsmul, CochainComplex.HomComplex.Cochain.map_ofHom, CochainComplex.HomComplex.CohomologyClass.toHom_mk_eq_zero_iff, summable_pow_mul_jacobiTheta₂_term_bound, CochainComplex.homologyMap_homologyδOfTriangle, DerivedCategory.triangleOfSES_obj₂, CochainComplex.shiftFunctorComm_hom_app_f, ediv_emod_unique'', CochainComplex.mappingCone.inl_v_snd_v, ComplexShape.instHasNoLoopIntUp, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_f, CochainComplex.HomComplex.Cochain.leftShiftAddEquiv_symm_apply, zpowersHom_ker_eq, CochainComplex.mappingCocone.inl_v_fst_f, CochainComplex.HomComplex.Cochain.rightShift_neg, CochainComplex.mappingCone.map_eq_mapOfHomotopy, CochainComplex.mappingConeCompTriangle_mor₃_naturality_assoc, HomotopyCategory.quotient_obj_singleFunctors_obj, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₃, DerivedCategory.instEssSurjCochainComplexIntQ, CochainComplex.HomComplex.Cochain.fromSingleMk_v_eq_zero, DerivedCategory.singleFunctorsPostcompQIso_hom_hom, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₂, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_precomp, CategoryTheory.Functor.mapCochainComplexShiftIso_hom_app_f, CochainComplex.shiftEval_inv_app, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁, CochainComplex.isKInjective_of_injective_aux, CochainComplex.mappingCocone.inr_v_descCochain_v_assoc, DerivedCategory.triangleOfSES_mor₂, CochainComplex.homologyMap_comp_eq_zero_of_distTriang_assoc, CategoryTheory.Abelian.SpectralObject.coreE₂Cohomological_i₀, HomotopyCategory.quotient_obj_mem_subcategoryAcyclic_iff_acyclic, ArithmeticFunction.abs_moebius_le_one, CochainComplex.HomComplex.Cocycle.rightShiftAddEquiv_apply, ideal_span_absNorm_eq_self, CochainComplex.ConnectData.homologyMap_map_of_eq_neg_succ, CochainComplex.HomComplex.Cocycle.fromSingleMk_mem_coboundaries_iff, CochainComplex.HomComplex.Cochain.equivHomotopy_symm_apply_hom, CochainComplex.Lifting.coe_cocycle₁'_v_comp_eq_zero, CochainComplex.HomComplex.Cocycle.equivHomShift_comp_shift, HomotopyCategory.homologyFunctor_shiftMap, CochainComplex.HomComplex.Cochain.rightShiftLinearEquiv_symm_apply, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₁, CochainComplex.mappingCone.lift_f_snd_v, CochainComplex.shiftShortComplexFunctorIso_zero_add_hom_app, CochainComplex.isKProjective_shift_iff, CochainComplex.instIsStrictlyLEObjIntSingleFunctor, ComplexShape.embeddingUpIntGE_f, CochainComplex.mappingCone.triangle_obj₂, CochainComplex.instIsStrictlyGEObjIntSingleFunctor, CochainComplex.mappingCone.triangleMap_hom₃, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₃, CategoryTheory.Functor.mapCochainComplexPlus_obj_obj_d, CochainComplex.mappingCocone.inl_v_descCochain_v_assoc, CochainComplex.mappingConeCompTriangle_mor₂, DerivedCategory.homologyFunctorFactorsh_inv_app_quotient_obj_assoc, CochainComplex.cm5b.degreewiseEpiWithInjectiveKernel_p, CochainComplex.HomComplex.Cochain.rightShift_v, CochainComplex.HomComplex.Cochain.rightUnshift_zero, CochainComplex.mappingConeCompTriangleh_comm₁, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_extMk, CochainComplex.HomComplex.Cocycle.toSingleMk_postcomp, HurwitzZeta.hasSum_int_completedCosZeta, CochainComplex.HomComplex.Cocycle.leftShift_coe, absNorm_under_eq_sInf, CochainComplex.HomComplex.Cochain.shift_v', Function.locallyFinsuppWithin.restrict_negPart, CochainComplex.cm5b.instInjectiveXIntMappingConeIdI, CochainComplex.Lifting.comp_coe_cocyle₁'_v_eq_zero_assoc, RootPairing.Base.abs_cartanMatrix_apply, DerivedCategory.homologyFunctorFactorsh_inv_app_quotient_obj, CochainComplex.mappingCocone.inl_v_desc_f_assoc, Valuation.IsRankOneDiscrete.generator_eq_neg_exp_one_of_surjective, DerivedCategory.mem_distTriang_iff, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_inv_assoc, ValueDistribution.logCounting_coe, cast_mem_ideal_iff, CategoryTheory.Functor.instCommShiftCochainComplexIntMapMap₂CochainComplex, abs_zsmul, HurwitzZeta.hasSum_int_completedSinZeta, CochainComplex.HomComplex.Cochain.rightShift_add, CochainComplex.ShiftSequence.shiftIso_inv_app, CochainComplex.HomComplex.Cochain.diff_v, DerivedCategory.instIsLEObjCochainComplexIntQOfIsLE, DerivedCategory.mappingCocone_triangle_distinguished, CategoryTheory.Functor.instCommShiftCochainComplexIntMapFlipMap₂CochainComplex, CochainComplex.mappingCocone.inl_v_snd_v_assoc, CochainComplex.HomComplex.Cochain.toSingleEquiv_toSingleMk, CochainComplex.isGE_shift, Polynomial.finite_abs_eval_le_of_degree_lt, CochainComplex.HomComplex.δ_neg_one_cochain, CochainComplex.HomComplex.Cochain.ofHoms_zero, DerivedCategory.Q_map_eq_of_homotopy, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_hom_app, CochainComplex.Lifting.coe_cocycle₁'_v_comp_eq_zero_assoc, CochainComplex.mappingCone.triangleRotateShortComplex_f, CochainComplex.HomComplex.Cocycle.fromSingleMk_postcomp, HomotopyCategory.quotient_obj_mem_subcategoryAcyclic_iff_exactAt, CochainComplex.HomComplex.Cocycle.rightUnshift_coe, CategoryTheory.Abelian.SpectralObject.coreE₂Cohomological_i₁, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃, CochainComplex.mappingCone.lift_f, CochainComplex.HomComplex.Cochain.δ_leftShift, DerivedCategory.isIso_Q_map_iff_quasiIso, Ideal.ringChar_quot, CochainComplex.HomComplex.Cocycle.toSingleMk_precomp, CochainComplex.HomComplex.CohomologyClass.toHom_mk, CochainComplex.HomComplex.Cochain.add_v, CochainComplex.πTruncGE_naturality_assoc, CochainComplex.HomComplex.Cocycle.leftShiftAddEquiv_apply, liesOver_span_absNorm, CochainComplex.instIsMultiplicativeIntDegreewiseEpiWithInjectiveKernel, DerivedCategory.left_fac_of_isStrictlyGE, CochainComplex.mappingConeHomOfDegreewiseSplitIso_hom_f, CochainComplex.mappingCone.inl_v_fst_v_assoc, CochainComplex.liftCycles_shift_homologyπ_assoc, CategoryTheory.ProjectiveResolution.cochainComplex_d_assoc, CochainComplex.mappingCocone.inr_v_descCochain_v, CochainComplex.HomComplex.Cochain.leftShift_neg, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom, abs_zsmul_eq_zero, CochainComplex.homologyFunctorFactors_hom_app_homologyδOfTriangle, CategoryTheory.Functor.mapDerivedCategoryFactorsh_hom_app, CochainComplex.HomComplex.Cochain.toSingleMk_sub, CochainComplex.Plus.instIsStableUnderShiftIntPlus, CochainComplex.HomComplex.Cocycle.equivHomShift_apply, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₁, sign_mul_abs, CategoryTheory.Functor.mapCochainComplexPlus_map_hom_f, CochainComplex.HomComplex.Cochain.leftUnshift_neg, CochainComplex.isLE_shift, CochainComplex.mappingCone.triangle_obj₁, Nat.absNorm_under_prime, CochainComplex.mappingCone.lift_f_snd_v_assoc, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₁, CochainComplex.mappingCone.mapHomologicalComplexXIso'_inv, ComplexShape.boundaryLE_embeddingUpIntLE_iff, CochainComplex.cm5b, LaurentPolynomial.antipode_C_mul_T, CategoryTheory.InjectiveResolution.Hom.ι'_comp_hom', CochainComplex.instQuasiIsoIntπTruncGEOfIsGE, CochainComplex.mappingCone.inr_f_desc_f_assoc, DerivedCategory.homologyFunctorFactors_hom_naturality_assoc, CategoryTheory.InjectiveResolution.extAddEquivCohomologyClass_symm_apply, CategoryTheory.InjectiveResolution.instInjectiveXIntCochainComplex, CochainComplex.shiftFunctor_obj_d, CochainComplex.HomComplex.Cochain.toSingleMk_precomp, CochainComplex.HomComplex.Cocycle.rightShift_coe, RootPairing.GeckConstruction.e_lie_u, AddSubgroup.fg_iff_exists_fin_addMonoidHom, CochainComplex.mappingCone.d_fst_v, CochainComplex.mappingConeCompHomotopyEquiv_hom_inv_id_assoc, CochainComplex.Plus.instIsStableUnderRetractsQuasiIso, Polynomial.abs_leadingCoeff_eq_one_of_mahlerMeasure_eq_one, CochainComplex.liftCycles_shift_homologyπ, abs_natCast, CochainComplex.HomComplex.Cochain.leftUnshift_zero, abs_eq_natAbs, DerivedCategory.left_fac, Rat.abs_def', CochainComplex.HomComplex.Cochain.comp_assoc_of_second_degree_eq_neg_third_degree, CochainComplex.mappingCone.triangle_obj₃, CochainComplex.HomComplex.Cochain.map_neg, CochainComplex.isZero_of_isLE, CochainComplex.HomComplex_d_hom_apply, CochainComplex.instFaithfulIntSingleFunctor, CochainComplex.HomComplex.CohomologyClass.homAddEquiv_apply, CochainComplex.mappingConeCompTriangle_obj₁, CochainComplex.cm5b.I_X, ZLattice.abs_repr_le, norm_jacobiTheta₂_term_fderiv_le, CategoryTheory.InjectiveResolution.extAddEquivCohomologyClass_apply, HomologicalComplex₂.ι_totalShift₁Iso_hom_f, zsmul_int_one, CategoryTheory.ShiftedHom.opEquiv'_add_symm, ComplexShape.instIsTruncGENatIntEmbeddingUpNat, CochainComplex.mappingCocone.lift_f_fst_f_assoc, CochainComplex.mappingCocone.inr_v_desc_f, natCast_natAbs, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, CochainComplex.ι_mapBifunctorShift₁Iso_hom_f, CochainComplex.ShiftSequence.shiftIso_hom_app, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_neg, ArithmeticFunction.abs_moebius, CochainComplex.HomComplex.Cochain.single_v_eq_zero, CategoryTheory.InjectiveResolution.cochainComplex_d, CochainComplex.mappingCone.map_δ, CochainComplex.HomComplex.Cochain.ofHom_comp, CochainComplex.HomComplex.Cochain.ofHomotopy_ofEq, CochainComplex.ConnectData.restrictionGEIso_hom_f
instAddMonoid 📖	CompOp	835 math math: CategoryTheory.Triangulated.SpectralObject.Hom.comm, HomotopyCategory.spectralObjectMappingCone_δ'_app, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_map_app_hom₃, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_eq, CategoryTheory.ShortComplex.ShortExact.instHasSmallLocalizedShiftedHomHomologicalComplexIntUpQuasiIsoX₃CochainComplexMapSingleFunctorOfNatX₁, CategoryTheory.Functor.mapTriangleIdIso_inv_app_hom₃, CochainComplex.HomComplex.Cochain.rightShiftAddEquiv_symm_apply, LaurentPolynomial.degree_C_mul_T_ite, CategoryTheory.Triangulated.Octahedron.mem, CategoryTheory.Triangulated.TStructure.truncGEδLT_comp_truncLTι, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.Triangulated.TStructure.truncGEπ_comp_truncGEδLT_assoc, Polynomial.toLaurent_eq_zero, CategoryTheory.Abelian.Ext.homLinearEquiv_apply, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_hom_app_eq, CochainComplex.HomComplex.Cocycle.leftShiftAddEquiv_symm_apply, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_map_app_hom₂, zpowersMulHom_symm_apply, LaurentPolynomial.mk'_mul_T, CochainComplex.mappingCocone.inl_v_descCochain_v, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₁, qExpansionRingHom_apply, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₃, AddCommGrpCat.asHom_hom_apply, CochainComplex.isStrictlyGE_shift, CochainComplex.mappingCone.id, CategoryTheory.Pretriangulated.Triangle.invRotate_obj₁, CochainComplex.shiftFunctorZero_eq, FreeAbelianGroup.toFinsupp_toFreeAbelianGroup, HomologicalComplex₂.totalShift₂Iso_hom_naturality_assoc, CochainComplex.mappingCone.liftCochain_v_snd_v_assoc, CochainComplex.HomComplex.Cochain.leftShift_smul, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₁, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app, CategoryTheory.Triangulated.Octahedron'.triangle_mor₃, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_inverse, Ring.ordFrac_eq_div, CategoryTheory.Pretriangulated.shiftFunctorZero_op_inv_app, CochainComplex.mappingCone.liftCochain_v_snd_v, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₂, CategoryTheory.Triangulated.TStructure.triangleLEGE_map_hom₃, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₃, CategoryTheory.Functor.mapTriangleCompIso_inv_app_hom₂, CategoryTheory.Triangulated.TStructure.instIsStableUnderShiftBoundedInt, NumberField.FinitePlace.norm_def', DerivedCategory.instCommShiftHomologicalComplexIntUpHomFunctorQuotientCompQhIso, CategoryTheory.Functor.mapTriangle_obj, CategoryTheory.Abelian.Ext.preadditiveYoneda_homologySequenceδ_singleTriangle_apply, CategoryTheory.Triangulated.Octahedron'.mem, CategoryTheory.ShiftedHom.opEquiv_symm_add, CategoryTheory.Functor.homologySequence_comp_assoc, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app, CategoryTheory.ObjectProperty.tStructure_isGE_iff, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_postcomp, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv, CategoryTheory.GradedObject.shiftFunctor_map_apply, CategoryTheory.Pretriangulated.Triangle.shift_distinguished, NumberField.HeightOneSpectrum.NumberField.toNNReal_valued_eq_adicAbv, CategoryTheory.ObjectProperty.IsTriangulated.toIsStableUnderShift, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_obj, CategoryTheory.Abelian.Ext.smul_hom, CochainComplex.instLinearIntFunctorSingleFunctors, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂_assoc, NumberField.HeightOneSpectrum.rankOne_hom'_def, zpowersHom_symm_apply, CochainComplex.HomComplex.CohomologyClass.equivOfIsKInjective_apply, CochainComplex.mappingCone.d_snd_v, CochainComplex.HomComplex.Cochain.rightUnshift_neg, HomologicalComplex₂.D₂_totalShift₁XIso_hom_assoc, Profinite.NobelingProof.instIsAddTorsionFreeLocallyConstantInt, CategoryTheory.Adjunction.IsTriangulated.id, HomologicalComplex₂.D₂_totalShift₂XIso_hom_assoc, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_flip_hom_app, CategoryTheory.Functor.mapTriangleCommShiftIso_inv_app_hom₁, CochainComplex.mappingConeCompTriangle_mor₃, CochainComplex.HomComplex.Cochain.shift_add, CategoryTheory.Functor.homologySequence_comp, CochainComplex.HomComplex.Cochain.comp_id, CategoryTheory.Triangulated.SpectralObject.ω₂_obj_mor₃, CategoryTheory.Triangulated.TStructure.triangleω₁δ_map_hom₁, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₂_assoc, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁_assoc, CochainComplex.shiftShortComplexFunctorIso_add'_hom_app, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_hom_app, Ring.ordFrac_eq_ord, DerivedCategory.singleFunctorsPostcompQIso_inv_hom, CochainComplex.instIsCompatibleWithShiftHomologicalComplexIntUpQuasiIso, CategoryTheory.Functor.mem_homologicalKernel_iff, CategoryTheory.Functor.mapTriangleCompIso_hom_app_hom₂, LaurentPolynomial.T_pow, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app, uliftZPowersHom_symm_apply, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd_eq, CochainComplex.HomComplex.Cochain.leftShiftLinearEquiv_apply, CochainComplex.HomComplex.Cochain.shift_neg, Polynomial.trunc_toLaurent, CategoryTheory.Triangulated.AbelianSubcategory.exists_distinguished_triangle_of_epi, CategoryTheory.Triangulated.TStructure.ω₁δ_naturality_assoc, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f_assoc, HomologicalComplex₂.ι_totalShift₁Iso_hom_f_assoc, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₂, CategoryTheory.Pretriangulated.Triangle.functorMk_map_hom₃, CategoryTheory.Functor.homologySequenceδ_naturality, CochainComplex.HomComplex.Cochain.comp_zero_cochain_v, zmultiplesAddHom_symm_apply, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app, CochainComplex.HomComplex.Cocycle.equivHomShift'_symm_apply, LaurentPolynomial.eval₂_C_mul_T, Polynomial.toLaurent_C_mul_T, CochainComplex.mappingCone.inl_v_triangle_mor₃_f, CategoryTheory.Triangulated.TStructure.triangleω₁δ_map_hom₂, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_eq, CategoryTheory.Pretriangulated.Triangle.functorMk_map_hom₁, CochainComplex.XIsoOfEq_shift, HomologicalComplex₂.ι_totalShift₁Iso_inv_f, CategoryTheory.Triangulated.TStructure.truncGEπ_comp_truncGEδLT_app_assoc, CochainComplex.HomComplex.Cochain.ext₀_iff, CochainComplex.HomComplex.Cochain.rightUnshift_comp, CochainComplex.HomComplex.Cochain.rightUnshift_units_smul, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality_assoc, CochainComplex.mappingCone.inr_triangleδ, CategoryTheory.Pretriangulated.TriangleMorphism.comm₃, CochainComplex.HomComplex.Cochain.ofHoms_comp, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_eq, DerivedCategory.shiftMap_homologyFunctor_map_Q_assoc, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app_assoc, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₁, zpowersHom_apply, LaurentPolynomial.algebraMap_apply, CategoryTheory.Triangulated.TStructure.isGE_shift_iff, CochainComplex.mappingCone.id_X, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CochainComplex.HomComplex.CohomologyClass.bijective_toSmallShiftedHom_of_isKProjective, CategoryTheory.Functor.shift_map_op_assoc, CategoryTheory.Abelian.Ext.mk₀_hom, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality, CategoryTheory.Triangulated.TStructure.triangleLEGT_map_hom₁, CategoryTheory.Triangulated.TStructure.truncGEδLT_comp_truncLTι_app, CategoryTheory.Triangulated.Octahedron'.comm₂, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app_assoc, CategoryTheory.Triangulated.TStructure.isIso_truncLT_map_iff, CochainComplex.mappingConeCompHomotopyEquiv_comm₂_assoc, CochainComplex.HomComplex.CohomologyClass.bijective_toSmallShiftedHom_of_isKInjective, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_naturality, CategoryTheory.Pretriangulated.shiftFunctorAdd'_op_inv_app, qExpansion_of_mul, CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHom_mk, LaurentPolynomial.smeval_C_mul, HomotopyCategory.instAdditiveIntUpShiftFunctor, Padic.norm_eq_zpow_log_mulValuation, CochainComplex.HomComplex.Cochain.fromSingleMk_postcomp, CochainComplex.mappingCone.d_snd_v'_assoc, WithZeroMulInt.toNNReal_pos, LocallyFiniteOrder.orderAddMonoidHom_bijective, CategoryTheory.Abelian.Ext.preadditiveCoyoneda_homologySequenceδ_singleTriangle_apply, CochainComplex.HomComplex.Cochain.shift_zero, Subgroup.range_zpowersHom, CategoryTheory.Functor.instCommShiftHomotopyCategoryIntUpDerivedCategoryHomMapDerivedCategoryFactorsh, CochainComplex.shiftFunctorZero_inv_app_f, HomologicalComplex₂.ι_totalShift₂Iso_inv_f_assoc, CochainComplex.HomComplex.Cochain.leftShift_comp, CategoryTheory.Triangulated.Localization.instAdditiveLocalization'ShiftFunctorInt, Polynomial.toLaurent_injective, NumberField.HeightOneSpectrum.adicAbv_def, CategoryTheory.Triangulated.TStructure.triangleLTLTGELT_map_hom₁, zpowersMulHom_apply, CategoryTheory.Adjunction.IsTriangulated.commShift, CochainComplex.HomComplex.Cochain.zero_cochain_comp_v, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_inv_app_unop, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₃, CochainComplex.homologyFunctor_shift, Finsupp.toFreeAbelianGroup_comp_singleAddHom, CochainComplex.isKInjective_shift_iff, LaurentPolynomial.degree_C_mul_T, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_hom_app, WithZeroMulInt.toNNReal_lt_one_iff, CategoryTheory.Triangulated.Octahedron.comm₄_assoc, CochainComplex.HomComplex.Cochain.leftShift_rightShift_eq_negOnePow_rightShift_leftShift, DerivedCategory.shiftMap_homologyFunctor_map_Qh_assoc, CochainComplex.mappingCocone.id_X, HomotopyCategory.Pretriangulated.complete_distinguished_triangle_morphism, LaurentPolynomial.smeval_C, CategoryTheory.Triangulated.TStructure.isLE_shift_iff, CochainComplex.HomComplex.Cochain.leftShift_rightShift, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_naturality_assoc, HomologicalComplex₂.instHasTotalIntObjUpShiftFunctor₂, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_shift, nsmul_eq_mul, FreeAbelianGroup.equivFinsupp_symm_apply, NumberField.HeightOneSpectrum.NumberField.rankOne_hom'_def, AddCommGroup.equiv_free_prod_directSum_zmod, LaurentPolynomial.degree_C, LaurentPolynomial.eval₂_T, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₁, LaurentPolynomial.C_apply, CategoryTheory.Pretriangulated.Triangle.rotate_mor₃, CochainComplex.instAdditiveIntFunctorSingleFunctors, CategoryTheory.Abelian.Ext.singleFunctor_map_comp_hom, LaurentSeries.exists_ratFunc_val_lt, toAdd_pow, CategoryTheory.Triangulated.Localization.complete_distinguished_triangle_morphism, CategoryTheory.Triangulated.TStructure.exists_triangle, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₂, LocallyFiniteOrder.orderAddMonoidHom_strictMono, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj_assoc, CategoryTheory.ProjectiveResolution.extMk_hom, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_inv_hom₃, Polynomial.toLaurent_comp_C, CategoryTheory.Functor.mapTriangleCompIso_inv_app_hom₃, CategoryTheory.Triangulated.Octahedron.triangle_mor₃, CategoryTheory.Abelian.Ext.mapExactFunctor_hom, CochainComplex.HomComplex.Cochain.shift_smul, FreeAbelianGroup.toFinsupp_comp_toFreeAbelianGroup, CategoryTheory.Pretriangulated.Opposite.contractibleTriangleIso_hom_hom₃, CategoryTheory.Functor.mapTriangleCompIso_hom_app_hom₃, CategoryTheory.Triangulated.Octahedron.map_m₃, CategoryTheory.Triangulated.TStructure.triangleω₁δ_map_hom₃, CochainComplex.HomComplex.Cochain.leftShiftAddEquiv_apply, HomologicalComplex₂.instHasTotalIntObjUpCompShiftFunctor₁ShiftFunctor₂, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app, CategoryTheory.Pretriangulated.Triangle.distinguished_iff_of_isZero₂, CategoryTheory.MorphismProperty.IsCompatibleWithTriangulation.toIsCompatibleWithShift, Finsupp.toFreeAbelianGroup_single, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₁, CategoryTheory.Triangulated.TStructure.triangleLTLTGELT_obj_mor₃, CategoryTheory.Abelian.Ext.homEquiv_chgUniv, CategoryTheory.Pretriangulated.Triangle.shift_distinguished_iff, LaurentPolynomial.mk'_eq, CochainComplex.HomComplex.Cochain.rightShiftAddEquiv_apply, WithZeroMulInt.toNNReal_neg_apply, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv, CochainComplex.HomComplex.Cochain.leftUnshift_v, CategoryTheory.Functor.map_shift_unop, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₂, CategoryTheory.Functor.homologySequence_epi_shift_map_mor₁_iff, AddSubgroup.range_zmultiplesHom, CochainComplex.mappingCone.inl_snd, CategoryTheory.Triangulated.TStructure.triangleLEGT_obj_mor₃, zmultiplesHom_ker_eq, CategoryTheory.Pretriangulated.invRotate_map_hom₁, CategoryTheory.Functor.op_commShiftIso_hom_app_assoc, CochainComplex.HomComplex.Cochain.rightShift_leftShift, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_inv_app, CochainComplex.HomComplex.CohomologyClass.equivOfIsKInjective_symm_apply, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalence_counitIso_inv_app_assoc, CochainComplex.mappingCocone.liftCochain_comp_fst, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₃₁, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_of_epi₂, LaurentSeries.exists_Polynomial_intValuation_lt, CochainComplex.mappingCone.inl_desc, CochainComplex.HomComplex.Cochain.ofHom_v, CategoryTheory.Functor.homologySequence_exact₂, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom, CochainComplex.instLinearHomologicalComplexIntUpShiftFunctor, CategoryTheory.Functor.mapTriangle_map_hom₁, CategoryTheory.Triangulated.TStructure.isLE_shift, CategoryTheory.Pretriangulated.contractible_distinguished₂, CochainComplex.HomComplex.Cochain.leftUnshift_smul, CochainComplex.mappingCone.inr_f_snd_v, CategoryTheory.Triangulated.TStructure.instIsStableUnderShiftPlusInt, CategoryTheory.ObjectProperty.instIsCompatibleWithShiftTrWIntOfIsStableUnderShift, CochainComplex.instIsKInjectiveObjIntShiftFunctor, CochainComplex.mappingConeCompTriangle_mor₃_naturality, CategoryTheory.Functor.instCommShiftCochainComplexIntDerivedCategoryHomMapDerivedCategoryFactors, CategoryTheory.Functor.homologySequenceδ_comp_assoc, Polynomial.toLaurent_apply, CochainComplex.HomComplex.Cochain.shiftLinearMap_apply, CochainComplex.HomComplex.δ_comp_ofHom, CategoryTheory.Functor.homologySequence_mono_shift_map_mor₁_iff, CochainComplex.HomComplex.Cochain.comp_assoc_of_first_is_zero_cochain, CochainComplex.mappingCone.ofHom_lift, HomologicalComplex₂.D₁_totalShift₂XIso_hom_assoc, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app_assoc, CategoryTheory.Pretriangulated.preadditiveYoneda_homologySequenceδ_apply, ZMod.lift_castAddHom, CategoryTheory.ObjectProperty.instIsStableUnderShiftExtensionProductIterInt_1, CochainComplex.shiftFunctor_map_f', CochainComplex.mappingCone.ext_to_iff, CochainComplex.HomComplex.Cochain.rightShift_zero, CategoryTheory.Equivalence.IsTriangulated.trans, CochainComplex.mappingCone.lift_fst, ZMod.lift_comp_coe, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₃, CategoryTheory.Triangulated.TStructure.shift_le, CategoryTheory.Pretriangulated.Triangle.isZero₂_iff_isIso₃, WithZeroMulInt.toNNReal_le_one_iff, CochainComplex.quasiIso_shift_iff, CochainComplex.HomComplex.Cochain.rightUnshift_v, CochainComplex.mappingCone.ext_cochain_to_iff, coe_castAddHom, LaurentPolynomial.algebraMap_X_pow, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₂, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₃, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app_assoc, CochainComplex.shiftFunctorAdd'_inv_app_f', CategoryTheory.Abelian.Ext.hom_comp_singleFunctor_map_shift, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_inv_f_f, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app, CategoryTheory.Functor.mapTriangleCommShiftIso_hom_app_hom₃, CochainComplex.HomComplex.Cochain.ofHoms_v, FreeAbelianGroup.toFinsupp_of, CategoryTheory.Functor.mapCochainComplexShiftIso_inv_app_f, CochainComplex.shiftFunctorAdd'_eq, HomologicalComplex₂.D₁_totalShift₁XIso_hom_assoc, HomotopyCategory.instLinearIntUpShiftFunctor, CategoryTheory.Functor.mapTriangleCommShiftIso_inv_app_hom₃, CochainComplex.HomComplex.CohomologyClass.equiv_toSmallShiftedHom_mk, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_hom_app, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂, CategoryTheory.Functor.comp_homologySequenceδ, LaurentPolynomial.algebraMap_eq_toLaurent, CategoryTheory.Triangulated.TStructure.triangleLTGE_map_hom₃, CochainComplex.mappingCone.decomp_from, CochainComplex.mappingCone.inl_v_triangle_mor₃_f_assoc, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₁, CategoryTheory.Pretriangulated.Opposite.commShift_natTrans_op_int, HomotopyCategory.Pretriangulated.distinguished_cocone_triangle, HomologicalComplex₂.instHasTotalIntObjUpCompShiftFunctor₂ShiftFunctor₁, Polynomial.toLaurent_X_pow, CochainComplex.mappingCone.inr_triangleδ_assoc, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_map_app_hom₁, CochainComplex.HomComplex.Cochain.leftShift_zero, CochainComplex.mappingCone.inl_v_snd_v_assoc, zmultiplesHom_bijective, CochainComplex.HomComplex.δ_ofHom_comp, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_eq, CochainComplex.mappingCone.inr_f_triangle_mor₃_f, CategoryTheory.Pretriangulated.shiftFunctorZero_op_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_hom_f_f, CategoryTheory.Functor.complete_distinguished_essImageDistTriang_morphism, CategoryTheory.Abelian.Ext.homAddEquiv_apply, CategoryTheory.Functor.op_commShiftIso_inv_app_assoc, CategoryTheory.Functor.homologySequence_exact₃, LaurentPolynomial.single_eq_C, HomologicalComplex₂.ι_totalShift₁Iso_inv_f_assoc, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_obj_map_hom₃, CochainComplex.HomComplex.Cocycle.leftUnshift_coe, CategoryTheory.Triangulated.TStructure.le_shift, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₂₃, LaurentPolynomial.isUnit_T, CochainComplex.mappingCone.d_snd_v_assoc, CategoryTheory.HasExt.hasSmallLocalizedShiftedHom_of_isLE_of_isGE, DerivedCategory.instAdditiveShiftFunctorInt, CochainComplex.quasiIsoAt_shift_iff, CochainComplex.mappingCone.d_snd_v', CochainComplex.HomComplex.Cocycle.equivHomShift_symm_apply, CategoryTheory.ObjectProperty.trW_iff', CochainComplex.instIsKProjectiveObjIntShiftFunctor, tendsto_zmultiplesHom_cofinite, CochainComplex.mappingCocone.inl_v_snd_v, FreeAbelianGroup.notMem_support_iff, CategoryTheory.HasExt.instHasSmallLocalizedShiftedHomHomologicalComplexIntUpQuasiIsoOfIsGEOfIsLEOfNat, CategoryTheory.Functor.mapTriangleInvRotateIso_inv_app_hom₁, CochainComplex.HomComplex.Cochain.rightShift_smul, NumberField.FinitePlace.norm_def_int, FreeAbelianGroup.equivFinsupp_apply, CochainComplex.HomComplex.Cocycle.homOf_f, CategoryTheory.Functor.mapTriangleRotateIso_hom_app_hom₃, CategoryTheory.ObjectProperty.instIsTriangulatedFullSubcategoryι, CochainComplex.homOfDegreewiseSplit_f, CochainComplex.shiftFunctorAdd_inv_app_f, CategoryTheory.Triangulated.Octahedron.map_m₁, CategoryTheory.Abelian.Ext.add_hom, HomologicalComplex₂.ι_totalShift₂Iso_hom_f_assoc, CategoryTheory.Triangulated.Localization.instAdditiveLocalizationShiftFunctorInt, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₁, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₂, LaurentPolynomial.eval₂_C_mul_T_neg_n, CochainComplex.mappingCone.δ_snd, CategoryTheory.ObjectProperty.hasInducedTStructure_iff, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_inv_app, ZMod.lift_comp_castAddHom, CategoryTheory.Triangulated.SpectralObject.Hom.comm_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality_assoc, CategoryTheory.Pretriangulated.rotate_map_hom₃, CochainComplex.mappingCone.ext_cochain_from_iff, CategoryTheory.Functor.op_commShiftIso_inv_app, CategoryTheory.Triangulated.TStructure.triangleLTLTGELT_map_hom₂, CategoryTheory.ShiftedHom.opEquiv'_symm_apply, IsModuleFiltration.mk_int, CategoryTheory.Functor.mapTriangleIdIso_hom_app_hom₃, CategoryTheory.Adjunction.IsTriangulated.comp, CategoryTheory.Triangulated.TStructure.shift_ge, CategoryTheory.Pretriangulated.instCommShiftOppositeOpOpEquivalenceInt, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_inv_app_f, CategoryTheory.ObjectProperty.extensionProduct_iff, CategoryTheory.Pretriangulated.binaryProductTriangle_mor₃, LaurentPolynomial.C_eq_algebraMap, CategoryTheory.Pretriangulated.Opposite.commShift_adjunction_op_int, CochainComplex.HomComplex.Cocycle.rightShiftAddEquiv_symm_apply, CategoryTheory.Triangulated.TStructure.triangleLTGE_map_hom₂, CochainComplex.HomComplex.Cochain.shift_units_smul, CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_inv_app, CategoryTheory.Triangulated.Localization.instIsTriangulatedLocalization, CategoryTheory.Equivalence.IsTriangulated.instIsTriangulatedFunctorSymmOfInverse, CochainComplex.shiftFunctorAdd_eq, CochainComplex.HomComplex.Cochain.leftShiftLinearEquiv_symm_apply, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f, CategoryTheory.Pretriangulated.distinguished_cocone_triangle, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₃, HomologicalComplex₂.D₁_totalShift₁XIso_hom, HomologicalComplex₂.D₂_totalShift₁XIso_hom, CochainComplex.mappingCone.liftCochain_snd, LaurentPolynomial.single_eq_C_mul_T, MonoidHom.apply_mint, CategoryTheory.Triangulated.TStructure.exists_triangle_zero_one, CategoryTheory.Triangulated.TStructure.triangleLTGE_obj_mor₃, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₁, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality_assoc, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₂, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app_assoc, CategoryTheory.Abelian.Ext.zero_hom, LaurentPolynomial.comul_C, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_obj, LaurentPolynomial.eval₂_C, CochainComplex.mappingConeCompHomotopyEquiv_comm₂, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₂₃_assoc, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop, CategoryTheory.Pretriangulated.TriangleMorphism.comm₃_assoc, CochainComplex.HomComplex.δ_zero_cochain_v, CategoryTheory.Triangulated.TStructure.truncGEδLT_comp_natTransTruncLTOfLE_app, CochainComplex.HomComplex.CohomologyClass.toHom_bijective, CategoryTheory.Triangulated.SpectralObject.distinguished', LaurentPolynomial.eval₂_toLaurent, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop_assoc, ZMod.lift_coe, CochainComplex.HomComplex.Cochain.fromSingleMk_precomp, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_naturality, CategoryTheory.Pretriangulated.distinguished_cocone_triangle₁, CochainComplex.HomComplex.Cochain.leftUnshift_add, CategoryTheory.ObjectProperty.tStructure_isLE_iff, CategoryTheory.Pretriangulated.Triangle.π₃Toπ₁_app, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃_assoc, HomotopyCategory.instIsCompatibleWithShiftHomologicalComplexIntUpHomotopic, Finsupp.toFreeAbelianGroup_toFinsupp, LaurentPolynomial.invert_symm, CategoryTheory.Triangulated.TStructure.isIso_truncGT_map_iff, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₃, DerivedCategory.instLinearShiftFunctorInt, CochainComplex.HomComplex.Cochain.rightShift_units_smul, CategoryTheory.instHasSmallLocalizedShiftedHomHomologicalComplexIntUpQuasiIsoObjCochainComplexCompSingleFunctorOfNatOfHasExt, CategoryTheory.Triangulated.AbelianSubcategory.eq_zero_of_hom_shift_pos, IsRingFiltration.mk_int, CategoryTheory.Pretriangulated.Triangle.rotate_obj₃, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₁, LaurentPolynomial.toLaurent_support, CochainComplex.HomComplex.Cochain.rightUnshift_smul, CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ, CategoryTheory.Functor.mapTriangleCompIso_inv_app_hom₁, CategoryTheory.Triangulated.TStructure.triangleLEGE_map_hom₁, CategoryTheory.Triangulated.TStructure.triangleLTLTGELT_map_hom₃, uliftZMultiplesHom_apply_apply, CategoryTheory.Functor.IsTriangulated.instId, CochainComplex.HomComplex.Cocycle.equivHomShift'_apply, LocallyFiniteOrder.orderAddMonoidHom_apply, CochainComplex.instQuasiIsoIntMapHomologicalComplexUpShiftFunctor, CategoryTheory.Pretriangulated.binaryBiproductTriangle_mor₃, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃_assoc, CategoryTheory.Pretriangulated.Triangle.functorMk_map_hom₂, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_assoc, CategoryTheory.ShiftedHom.opEquiv_symm_apply_comp, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₁, CategoryTheory.Triangulated.TStructure.truncGEδLT_comp_truncLTι_assoc, CategoryTheory.Functor.mapTriangle_map_hom₃, CochainComplex.HomComplex.Cochain.δ_shift, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₃, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_iff_epi₂, HomologicalComplex₂.totalShift₁Iso_trans_totalShift₂Iso, CategoryTheory.ShiftedHom.opEquiv'_symm_add, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_flip_inv_app, addSubmonoid_closure_range_pow, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₃, CochainComplex.mappingCocone.inl_v_fst_f_assoc, CochainComplex.mappingCone.lift_snd, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_eq, CategoryTheory.ShiftedHom.opEquiv'_zero_add_symm, CategoryTheory.ShiftedHom.opEquiv'_symm_op_opShiftFunctorEquivalence_counitIso_inv_app_op_shift, CategoryTheory.Pretriangulated.Opposite.distinguished_cocone_triangle, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_hom_app_unop_assoc, MonoidHom.ext_mint_iff, CategoryTheory.Pretriangulated.Triangle.mono₃, CategoryTheory.Functor.shift_map_op, CategoryTheory.Functor.mapTriangleCommShiftIso_inv_app_hom₂, DerivedCategory.shift_homologyFunctor, CategoryTheory.InjectiveResolution.extMk_hom, CategoryTheory.Pretriangulated.shiftFunctor_op_map, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_inv_app_eq, WithZeroMulInt.toNNReal_eq_one_iff, CategoryTheory.Pretriangulated.productTriangle_mor₃, AddMonoidHom.ext_int_iff, CochainComplex.cm5b.i_f_comp, CochainComplex.HomComplex.Cochain.δ_rightUnshift, Polynomial.toLaurent_inj, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZero_eq, CochainComplex.mappingCone.inr_snd, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_obj, CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app, CochainComplex.HomComplex.Cochain.leftUnshift_units_smul, CochainComplex.HomComplex.Cochain.rightShiftLinearEquiv_apply, CochainComplex.HomComplex.Cocycle.shift_coe, CategoryTheory.Functor.homologySequence_exact₁, LaurentPolynomial.invert_apply, CategoryTheory.Functor.mapTriangleCompIso_hom_app_hom₁, CochainComplex.mappingCone.lift_desc_f, CochainComplex.isStrictlyLE_shift, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₃₁_assoc, CategoryTheory.Triangulated.TStructure.isIso_truncLE_map_iff, CochainComplex.mappingCone.δ_liftCochain, ZMod.lift_injective, CategoryTheory.Triangulated.SpectralObject.mapTriangulatedFunctor_δ', LaurentPolynomial.counit_C_mul_T, CochainComplex.HomComplex.Cochain.δ_rightShift, zmultiplesHom_apply, HomologicalComplex₂.ι_totalShift₂Iso_inv_f, CochainComplex.HomComplex.Cochain.leftShift_v, CochainComplex.mappingCone.desc_f, CochainComplex.HomComplex.Cochain.rightUnshift_add, CategoryTheory.Pretriangulated.Triangle.epi₃, Polynomial.toLaurent_one, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_hom_f_f, HomotopyCategory.homologyFunctor_shiftMap_assoc, HomologicalComplex₂.totalShift₂Iso_hom_naturality, CategoryTheory.Triangulated.TStructure.truncGEπ_comp_truncGEδLT, CategoryTheory.Pretriangulated.contractibleTriangle_mor₃, LaurentPolynomial.degree_C_ite, CochainComplex.shiftFunctor_obj_X', CochainComplex.HomComplex.Cochain.shift_v, ComplexShape.σ_def, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₃, CochainComplex.shiftFunctorZero_hom_app_f, LaurentPolynomial.eval₂_T_neg_n, CategoryTheory.Triangulated.TStructure.ω₁δ_app, DerivedCategory.shiftMap_homologyFunctor_map_Q, CategoryTheory.ShiftedHom.opEquiv'_symm_comp, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_eq, CategoryTheory.Equivalence.IsTriangulated.instIsTriangulatedInverseSymmOfFunctor, CochainComplex.mappingCone.inr_f_snd_v_assoc, CategoryTheory.Abelian.Ext.neg_hom, CategoryTheory.Triangulated.TStructure.triangleω₁δ_obj_mor₃, CategoryTheory.Functor.mapTriangleCommShiftIso_hom_app_hom₁, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv_assoc, CochainComplex.HomComplex.Cochain.shiftAddHom_apply, WithZeroMulInt.toNNReal_strictMono, CochainComplex.HomComplex.Cochain.δ_leftUnshift, LaurentPolynomial.antipode_C, CochainComplex.HomComplex.CohomologyClass.equivOfIsKProjective_symm_apply, CategoryTheory.Pretriangulated.commShiftIso_opOp_inv_app_assoc, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_inv_app_assoc, CochainComplex.shiftFunctorAdd'_hom_app_f', CochainComplex.HomComplex.Cochain.leftShift_add, CategoryTheory.Triangulated.TStructure.truncGEδLT_comp_whiskerRight_natTransTruncLTOfLE_assoc, CategoryTheory.ObjectProperty.HasInducedTStructure.exists_triangle_zero_one, CochainComplex.HomComplex.Cochain.leftShift_comp_zero_cochain, CochainComplex.mappingCocone.δ_descCochain, CategoryTheory.Functor.map_shift_unop_assoc, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₁, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₃_assoc, CategoryTheory.Triangulated.Octahedron.comm₂, CochainComplex.shiftEval_hom_app, CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_assoc, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃, CochainComplex.instHasMapBifunctorObjIntShiftFunctor_1, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_inv_app_assoc, CochainComplex.HomComplex.Cocycle.equivHomShift_comp, CochainComplex.cm5b.i_f_comp_assoc, LocallyFiniteOrder.orderAddMonoidHom_toAddMonoidHom, CategoryTheory.Triangulated.TStructure.truncGEδLT_comp_whiskerRight_natTransTruncLTOfLE, CochainComplex.shiftFunctor_obj_d', CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_hom_app, CochainComplex.instHasMapBifunctorObjIntShiftFunctor, CategoryTheory.Triangulated.TStructure.ge_shift, CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_iff_epi₃, CategoryTheory.Triangulated.instNonemptyOctahedron, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_hom_app_f, CategoryTheory.Triangulated.TStructure.instIsStableUnderShiftMinusInt, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom_assoc, CategoryTheory.Triangulated.Localization.distinguished_cocone_triangle, CochainComplex.ι_mapBifunctorShift₁Iso_hom_f_assoc, zpowersHom_bijective, LaurentPolynomial.support_C_mul_T_of_ne_zero, IsDedekindDomain.HeightOneSpectrum.adicCompletion_valueGroup_eq, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_inv_f_f, LocallyFiniteOrder.orderMonoidHom_strictMono, CochainComplex.HomComplex.Cochain.leftShift_units_smul, LaurentPolynomial.counit_C, CategoryTheory.Triangulated.Localization.instIsTriangulatedLocalization', NumberField.HeightOneSpectrum.NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, CochainComplex.HomComplex.δ_comp_zero_cocycle, HomotopyCategory.homologyShiftIso_hom_app, CochainComplex.shiftFunctorAdd_hom_app_f, DerivedCategory.Qh_obj_singleFunctors_obj, WithZeroMulInt.toNNReal_pos_apply, HomologicalComplex₂.totalShift₁Iso_hom_naturality_assoc, CochainComplex.mapBifunctorShift₁Iso_trans_mapBifunctorShift₂Iso, CategoryTheory.ShiftedHom.opEquiv_symm_apply, CochainComplex.mappingCocone.inl_comp_descCochain, CategoryTheory.Functor.mapTriangleIdIso_inv_app_hom₁, CochainComplex.HomComplex.Cochain.toSingleMk_postcomp, CategoryTheory.ShiftedHom.opEquiv'_apply, LaurentPolynomial.comul_C_mul_T, uliftZPowersHom_apply_apply, CochainComplex.HomComplex.Cochain.id_comp, CochainComplex.mappingCocone.inl_v_desc_f, LaurentPolynomial.smeval_C_mul_T_n, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₂, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₃, CochainComplex.mappingCone.inr_f_triangle_mor₃_f_assoc, CategoryTheory.hasExt_iff, HomologicalComplex₂.ι_totalShift₂Iso_hom_f, CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₂, LaurentPolynomial.leftInverse_trunc_toLaurent, HomologicalComplex₂.instHasTotalIntObjUpShiftFunctor₁, CochainComplex.HomComplex.Cochain.comp_assoc_of_third_is_zero_cochain, CategoryTheory.Functor.mapTriangleIdIso_inv_app_hom₂, CategoryTheory.Triangulated.Octahedron'.comm₃_assoc, CategoryTheory.Pretriangulated.complete_distinguished_triangle_morphism, CochainComplex.HomComplex.CohomologyClass.toHom_mk_eq_zero_iff, CategoryTheory.Pretriangulated.Triangle.isZero₃_iff, CategoryTheory.ObjectProperty.instIsTriangulatedFullSubcategory, LaurentPolynomial.smul_eq_C_mul, CategoryTheory.Triangulated.TStructure.triangleLTGE_map_hom₁, zmultiplesHom_symm_apply, CategoryTheory.Equivalence.IsTriangulated.symm, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_inv_app_hom₃, CochainComplex.mappingCone.δ_descCochain, CategoryTheory.Triangulated.AbelianSubcategory.shift_ι_map_ιK_assoc, Polynomial.toLaurent_C_mul_eq, CochainComplex.mappingCone.inl_v_snd_v, CategoryTheory.Functor.mapTriangleRotateIso_inv_app_hom₃, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_f, CochainComplex.HomComplex.Cochain.leftShiftAddEquiv_symm_apply, zpowersHom_ker_eq, CochainComplex.mappingCocone.inl_v_fst_f, CochainComplex.HomComplex.Cochain.rightShift_neg, HomologicalComplex₂.totalShift₁Iso_hom_naturality, CochainComplex.mappingConeCompTriangle_mor₃_naturality_assoc, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop, LaurentPolynomial.eval₂_T_n, CochainComplex.HomComplex.δ_comp_zero_cochain, CategoryTheory.Pretriangulated.Opposite.instAdditiveOppositeShiftFunctorInt, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₃, CategoryTheory.Functor.homologySequenceδ_naturality_assoc, CategoryTheory.Triangulated.TStructure.isGE_shift, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_of_mono₁, DerivedCategory.singleFunctorsPostcompQIso_hom_hom, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₂, CategoryTheory.Pretriangulated.complete_distinguished_triangle_morphism₁, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_hom_app_assoc, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₂, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_precomp, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_obj_obj_mor₃, CategoryTheory.Pretriangulated.preadditiveYoneda_shiftMap_apply, CategoryTheory.MorphismProperty.IsCompatibleWithTriangulation.compatible_with_triangulation, CategoryTheory.Functor.mapCochainComplexShiftIso_hom_app_f, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_inv_app_unop_assoc, CochainComplex.shiftEval_inv_app, DerivedCategory.shiftMap_homologyFunctor_map_Qh, zmultiplesAddHom_apply, CategoryTheory.Triangulated.Octahedron'.comm₂_assoc, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁, LaurentPolynomial.trunc_C_mul_T, CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor_map_hom₁, LaurentPolynomial.support_C_mul_T, CategoryTheory.Triangulated.TStructure.truncGEδLT_comp_truncLTι_app_assoc, CategoryTheory.Functor.mapTriangleCommShiftIso_hom_app_hom₂, CochainComplex.HomComplex.Cocycle.rightShiftAddEquiv_apply, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₂, Polynomial.toLaurent_X, CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_iff_mono₃, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app, CategoryTheory.Triangulated.TStructure.triangleLEGT_map_hom₃, CochainComplex.mappingCocone.δ_liftCochain, CategoryTheory.ObjectProperty.instIsStableUnderShiftExtensionProductInt, ComplexShape.ε_up_ℤ, addSubmonoid_closure_range_mul_self, CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd'_hom_app_hom₂, CategoryTheory.Functor.op_commShiftIso_hom_app, CochainComplex.HomComplex.Cocycle.equivHomShift_comp_shift, HomotopyCategory.homologyFunctor_shiftMap, CategoryTheory.ObjectProperty.instIsStableUnderShiftExtensionProductIterInt, CochainComplex.HomComplex.Cochain.rightShiftLinearEquiv_symm_apply, CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_hom_app, CategoryTheory.Pretriangulated.Triangle.isZero₁_iff, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₁, CochainComplex.shiftShortComplexFunctorIso_zero_add_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv_assoc, CochainComplex.isKProjective_shift_iff, CategoryTheory.Functor.mapTriangleInvRotateIso_hom_app_hom₁, Polynomial.coe_toLaurentAlg, CochainComplex.mappingCone.inr_descCochain, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₃, CochainComplex.mappingCocone.inl_v_descCochain_v_assoc, HomologicalComplex₂.D₁_totalShift₂XIso_hom, CochainComplex.HomComplex.Cochain.rightShift_v, NumberField.HeightOneSpectrum.toNNReal_valued_eq_adicAbv, CochainComplex.HomComplex.Cochain.rightUnshift_zero, NumberField.FinitePlace.norm_embedding', CategoryTheory.InjectiveResolution.extEquivCohomologyClass_extMk, CategoryTheory.Equivalence.IsTriangulated.refl, LocallyFiniteOrder.orderMonoidWithZeroHom_strictMono, CategoryTheory.Pretriangulated.commShiftIso_unopUnop_hom_app_assoc, CochainComplex.HomComplex.Cocycle.leftShift_coe, HomologicalComplex₂.D₂_totalShift₂XIso_hom, CategoryTheory.Triangulated.TStructure.truncGELTδLT_app, CategoryTheory.Triangulated.TStructure.eTruncGEδLT_coe, CochainComplex.HomComplex.CohomologyClass.equivOfIsKProjective_apply, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_iff_mono₁, CategoryTheory.Abelian.Ext.homLinearEquiv_symm_apply, CochainComplex.HomComplex.Cochain.shift_v', CategoryTheory.Triangulated.SpectralObject.ω₂_map_hom₃, Polynomial.toLaurent_C, CategoryTheory.Triangulated.TStructure.ω₁δ_naturality, CategoryTheory.Triangulated.TStructure.truncGEπ_comp_truncGEδLT_app, CategoryTheory.Triangulated.TStructure.triangleLEGT_map_hom₂, Polynomial.toLaurentAlg_apply, CochainComplex.mappingCocone.inl_v_desc_f_assoc, CategoryTheory.Functor.instCommShiftCochainComplexIntMapMap₂CochainComplex, CategoryTheory.Pretriangulated.Opposite.complete_distinguished_triangle_morphism, CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_hom_app_unop_assoc, CategoryTheory.ObjectProperty.trW.shift, CochainComplex.HomComplex.Cochain.rightShift_add, Polynomial.toLaurent_C_mul_X_pow, CochainComplex.ShiftSequence.shiftIso_inv_app, CategoryTheory.Triangulated.Octahedron'.comm₃, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_functor, LaurentPolynomial.eval₂_C_mul_T_n, CategoryTheory.Triangulated.Octahedron.comm₄, CategoryTheory.Functor.instCommShiftCochainComplexIntMapFlipMap₂CochainComplex, CochainComplex.mappingCocone.inl_v_snd_v_assoc, LaurentPolynomial.toLaurent_reverse, CochainComplex.isGE_shift, LocallyFiniteOrder.orderAddMonoidEquiv_apply, CategoryTheory.Triangulated.TStructure.triangleLEGE_obj_mor₃, CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₂, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_hom_app, Valued.exists_pow_lt_of_le_exp_neg_one, qExpansion_of_pow, CochainComplex.Lifting.comp_coe_cocycle₁_comp, CategoryTheory.Pretriangulated.contractible_distinguished₁, CochainComplex.HomComplex.Cocycle.rightUnshift_coe, CategoryTheory.Pretriangulated.productTriangle.zero₃₁, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃, CochainComplex.mappingCone.lift_f, CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse_map, CochainComplex.HomComplex.Cochain.δ_leftShift, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_hom_app_eq, CochainComplex.HomComplex.CohomologyClass.toHom_mk, CochainComplex.HomComplex.Cocycle.leftShiftAddEquiv_apply, LaurentPolynomial.comul_C_mul_T_self, CochainComplex.mappingConeHomOfDegreewiseSplitIso_hom_f, LaurentPolynomial.instIsScalarTowerPolynomial, CochainComplex.liftCycles_shift_homologyπ_assoc, LaurentPolynomial.invert_C, CategoryTheory.Triangulated.TStructure.truncGEδLT_comp_natTransTruncLTOfLE_app_assoc, CategoryTheory.Functor.mapTriangleIdIso_hom_app_hom₁, CategoryTheory.Functor.homologySequenceδ_comp, CochainComplex.HomComplex.δ_zero_cochain_comp, CategoryTheory.Pretriangulated.shift_unop_opShiftFunctorEquivalence_counitIso_inv_app, CategoryTheory.Functor.mapTriangleIdIso_hom_app_hom₂, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop, CategoryTheory.Triangulated.TStructure.triangleLEGE_map_hom₂, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app, CategoryTheory.Triangulated.AbelianSubcategory.shift_ι_map_ιK, NumberField.FinitePlace.norm_embedding_int, CochainComplex.HomComplex.Cochain.leftShift_neg, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom, CochainComplex.HomComplex.Cochain.comp_assoc_of_second_is_zero_cochain, CochainComplex.Plus.instIsStableUnderShiftIntPlus, CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_hom_app_unop, AddMonoidHom.apply_int, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_obj_map_hom₂, CochainComplex.HomComplex.Cocycle.equivHomShift_apply, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₁, LaurentPolynomial.exists_T_pow, CategoryTheory.Triangulated.TStructure.eTriangleLTGE_obj_map_hom₁, CochainComplex.HomComplex.Cochain.leftUnshift_neg, CochainComplex.isLE_shift, CategoryTheory.Functor.homologySequence_mono_shift_map_mor₂_iff, CochainComplex.mappingCone.inr_fst, castAddHom_int, LaurentPolynomial.invert_comp_C, CategoryTheory.Pretriangulated.Triangle.functorMk_obj, LaurentPolynomial.antipode_C_mul_T, CategoryTheory.Functor.comp_homologySequenceδ_assoc, LaurentPolynomial.degree_C_le, CategoryTheory.Pretriangulated.Triangle.coyoneda_exact₁, NumberField.FinitePlace.norm_def, CategoryTheory.GradedObject.shiftFunctor_obj_apply, CochainComplex.HomComplex.Cochain.toSingleMk_precomp, CochainComplex.HomComplex.Cocycle.rightShift_coe, AddSubgroup.fg_iff_exists_fin_addMonoidHom, CategoryTheory.Functor.mem_homologicalKernel_trW_iff, Finsupp.toFreeAbelianGroup_comp_toFinsupp, CochainComplex.liftCycles_shift_homologyπ, CochainComplex.HomComplex.Cochain.leftUnshift_zero, CategoryTheory.Functor.mapTriangle_map_hom₂, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop_assoc, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_naturality, CochainComplex.HomComplex.Cochain.comp_assoc_of_second_degree_eq_neg_third_degree, CategoryTheory.Pretriangulated.preadditiveCoyoneda_homologySequenceδ_apply, CategoryTheory.Triangulated.TStructure.isIso_truncGE_map_iff, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply_assoc, CochainComplex.HomComplex.CohomologyClass.homAddEquiv_apply, CategoryTheory.ObjectProperty.isTriangulated_lift, CategoryTheory.ObjectProperty.trW_iff, LaurentPolynomial.degree_C_mul_T_le, CategoryTheory.Functor.homologySequence_epi_shift_map_mor₂_iff, CochainComplex.instAdditiveHomologicalComplexIntUpShiftFunctor, HomologicalComplex₂.ι_totalShift₁Iso_hom_f, CategoryTheory.Pretriangulated.shiftFunctorCompIsoId_op_inv_app_assoc, CategoryTheory.ShiftedHom.opEquiv'_add_symm, CategoryTheory.Pretriangulated.Triangle.yoneda_exact₃, LaurentPolynomial.invert_T, EisensteinSeries.gammaSet_eq_gcd_mul_divIntMap, CochainComplex.ι_mapBifunctorShift₁Iso_hom_f, CochainComplex.ShiftSequence.shiftIso_hom_app, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_counitIso_hom_app_shift, CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_unitIso_inv_app_assoc, LaurentPolynomial.involutive_invert, CategoryTheory.Functor.IsTriangulated.instComp, CochainComplex.HomComplex.δ_zero_cocycle_comp, CategoryTheory.ShiftedHom.opEquiv_symm_comp, CategoryTheory.Triangulated.Octahedron.comm₂_assoc, HomotopyCategory.instCommShiftHomologicalComplexIntUpHomFunctorMapHomotopyCategoryFactors, CategoryTheory.Triangulated.TStructure.spectralObject_δ, CochainComplex.mappingCone.map_δ, CategoryTheory.Abelian.Ext.comp_hom, CochainComplex.HomComplex.Cochain.ofHom_comp, uliftZMultiplesHom_symm_apply
instAddSemigroup 📖	CompOp	—
instCommMonoid 📖	CompOp	41 math math: Multiset.prod_int_mod, ComplexShape.eulerCharSignsDownNat_χ, toMul_uzpow, uzpow_natCast, int_prod_range_pos, Finset.prod_indicator_biUnion_finset_sub_indicator, uzpow_coe_nat, Equiv.Perm.sign_eq_prod_prod_Ioi, ModEq.multisetProd_one, ComplexShape.ε_down_ℕ, Choose.lucas_theorem, Choose.choose_modEq_prod_range_choose, ModEq.prod, Equiv.Perm.sign_eq_prod_prod_Iio, NumberField.InfinitePlace.ComplexEmbedding.conjugate_sign, cast_multiset_prod, Polynomial.Chebyshev.iterate_derivative_U_eval_one_dvd, Polynomial.Chebyshev.iterate_derivative_T_eval_one_dvd, prod_modEq_single, negOnePow_def, int_prod_range_nonneg, Polynomial.Chebyshev.iterate_derivative_U_eval_one, ComplexShape.eulerCharSignsUpNat_χ, ModEq.multisetProd_map_one, uzpow_intCast, Polynomial.Chebyshev.iterate_derivative_U_eval_one_eq_div, Polynomial.Chebyshev.iterate_derivative_T_eval_one, Equiv.Perm.sign_prodCongrRight, Finset.prod_indicator_biUnion_sub_indicator, Nat.factorial_coe_dvd_prod, Equiv.Perm.sign_prodCongrLeft, prod_modEq_ite, Equiv.Perm.sign_of_cycleType', ModEq.multisetProd_map, Finset.prod_int_mod, ModEq.prod_one, cast_prod, Polynomial.Chebyshev.iterate_derivative_T_eval_one_eq_div, cast_finsuppProd, Equiv.Perm.OnCycleFactors.sign_kerParam_apply_apply, ofMul_uzpow
instCommSemigroup 📖	CompOp	—
instMonoid 📖	CompOp	538 math math: even_pow, Fin.sign_cycleIcc_of_eq, AlternatingMap.domCoprod.summand_mk'', Polynomial.ascPochhammer_smeval_neg_eq_descPochhammer, Matrix.det_apply, sq_eq_one_of_sq_le_three, jacobiSym.sq_one, ComplexShape.ε_succ, natCast_multiplicity, Polynomial.Chebyshev.U_eval_zero, List.alternatingSum_append, HNNExtension.toSubgroup_neg_one, Function.Antiperiodic.add_int_mul_eq, natAbs_le_self_pow_two, CochainComplex.HomComplex.Cochain.δ_single, numDerangements_succ, natAbs_eq_iff_associated, ZMod.neg_one_pow_div_two_of_three_mod_four, ComplexShape.χ_prev, padicValRat.padicValRat_le_padicValRat_iff, Polynomial.IsUnitTrinomial.coeff_isUnit, ComplexShape.EulerCharSigns.χ_next, ContinuousMultilinearMap.alternatization_apply_apply, AlternatingMap.map_perm, fib_succ_mul_fib_pred_sub_fib_sq, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₁, Equiv.Perm.sign_of_cycleType, Matrix.det_permute, IsCyclotomicExtension.discr_prime_pow_eq_unit_mul_pow, ComplexShape.eulerCharSignsDownNat_χ, AbsoluteValue.map_units_intCast, toMul_uzpow, List.alternatingProd_eq_finset_prod, ExteriorAlgebra.basis_mul_of_disjoint, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₃, ContinuousAlternatingMap.map_insertNth, uzpow_zero, even_pow', Matrix.detp_neg_one_one, Polynomial.coeff_shiftedLegendre, odd_pow', ComplexShape.associative_ε₂_ε₁, Equiv.Perm.signAux_swap, HomologicalComplex.mapBifunctor₂₃.d₂_eq, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_obj, alternating_sum_range_choose_of_ne, HNNExtension.NormalWord.ReducedWord.chain, uzpow_natCast, HomologicalComplex₂.totalAux.d₂_eq, Equiv.Perm.sign_subtypePerm, HomologicalComplex₂.D₂_totalShift₁XIso_hom_assoc, HNNExtension.NormalWord.t_smul_eq_unitsSMul, HomologicalComplex₂.D₂_totalShift₂XIso_hom_assoc, ZMod.neg_one_pow_div_two_of_one_mod_four, ComplexShape.ε_add, LucasLehmer.sMod_lt, natAbs_lt_iff_sq_lt, finiteMultiplicity_iff, PadicInt.pow_dvd_nthHom_sub, Polynomial.Chebyshev.T_eval_zero, negOnePow_eq_neg_one_iff, jacobiSym.pow_right, HomologicalComplex.mapBifunctor₂₃.d₃_eq, Finset.inclusion_exclusion_card_inf_compl, Function.Antiperiodic.sub_int_mul_eq, Pell.is_pell_solution_iff_mem_unitary, Equiv.Perm.sign_trans_trans_symm, ComplexShape.instHasNoLoopIntDown, fib_neg_natCast, Equiv.Perm.viaFintypeEmbedding_sign, LucasLehmer.sMod_mod, uzpow_coe_nat, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f_assoc, Equiv.Perm.sign_symm, ArithmeticFunction.moebius_sq, CochainComplex.HomComplex.δ_v, padicValRat.of_int_multiplicity, Ring.multichoose_neg_self, HomologicalComplex₂.ιTotal_totalFlipIso_f_inv_assoc, Fin.sign_cycleRange, Polynomial.Chebyshev.T_eval_two_mul_zero, Equiv.Perm.sign_eq_prod_prod_Ioi, Equiv.Perm.prod_Ioi_comp_eq_sign_mul_prod, alternating_sum_range_choose, HNNExtension.NormalWord.prod_cons, Polynomial.zero_le_negOnePow_mul_eval_of_le_roots_of_leadingCoeff_nonneg, alternatingGroup.normalClosure_swap_mul_swap_five, modularCyclotomicCharacter.pow_dvd_aux_pow_sub_aux_pow, Polynomial.Chebyshev.T_eval_neg, ComplexShape.ε₁_ε₂, uzpow_one, legendreSym.sq_one, HNNExtension.toSubgroupEquiv_neg_one, ofNat_isUnit, Equiv.Perm.sign_of_cycleType_eq_replicate, alternating_sum_range_choose_eq_choose, IsCyclotomicExtension.Rat.absdiscr_prime_pow, GradedTensorProduct.tmul_coe_mul_coe_tmul, uzpow_mul, ComplexShape.TensorSigns.ε'_succ, Rat.associated_num_den, ComplexShape.ε_down_ℕ, padicValInt_dvd_iff, AlternatingMap.alternatizeUncurryFin_apply, TotalComplexShapeSymmetry.σ_ε₁, fwdDiff_iter_eq_sum_shift, Equiv.Perm.decomposeFin.symm_sign, jacobiSym.pow_left, Polynomial.isUnitTrinomial_iff, HNNExtension.toSubgroup_one, CliffordAlgebra.map_mul_map_of_isOrtho_of_mem_evenOdd, Ring.choose_neg, HomologicalComplex₂.ι_totalShift₂Iso_inv_f_assoc, CochainComplex.HomComplex.Cochain.leftShift_comp, Polynomial.Chebyshev.U_eval_neg_one, negOnePow_two_mul, cast_pow, CategoryTheory.Preadditive.smul_iso_hom, AlternatingMap.map_congr_perm, ArithmeticFunction.moebius_apply_of_squarefree, isCoprime_of_sq_sum', cast_negOnePow, extDeriv_apply_vectorField, List.alternatingProd_append, Polynomial.smeval_neg_nat, emultiplicity_pow_sub_pow, Equiv.Perm.sign_prodExtendRight, qrSign.neg_one_pow, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, CochainComplex.HomComplex.Cochain.leftShift_rightShift_eq_negOnePow_rightShift_leftShift, CommRingCat.coproductCocone_inl, padicValInt_dvd_iff_of_ne_one, Equiv.Perm.sign_abs, Fin.sign_cycleIcc_of_ge, HNNExtension.NormalWord.prod_unitsSMul, HomologicalComplex₂.d₁_eq, CochainComplex.HomComplex.Cochain.leftShift_rightShift, Matrix.detp_one_one, ComplexShape.Associative.ε₂_ε₁, ComplexShape.ε₁_def, units_pow_two, CategoryTheory.Preadditive.smul_iso_inv, Ring.multichoose_neg_succ, units_inv_eq_self, LaurentSeries.derivative_iterate_coeff, MultilinearMap.domCoprod_alternization_coe, Matrix.det_eq_detp_sub_detp, IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_two, Equiv.Perm.sign_trans, abs_le_sqrt_iff_sq_le, Pell.exists_of_not_isSquare, negOnePow_add, sq_of_isCoprime, Equiv.Perm.signAux_one, Finset.inclusion_exclusion_sum_inf_compl, UnitsInt.univ, Equiv.Perm.sign_sumCongr, Equiv.Perm.sign_eq_prod_prod_Iio, HNNExtension.NormalWord.unitsSMul_cancels_iff, sq_eq_one_of_sq_lt_four, extDerivWithin_apply_vectorField_of_pairwise_commute, HNNExtension.NormalWord.ReducedWord.empty_toList, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₁, Matrix.det_permutation, AlternatingMap.neg_one_pow_smul_map_removeNth_add_eq_zero_of_eq, CochainComplex.HomComplex.Cochain.leftUnshift_v, NumberField.InfinitePlace.ComplexEmbedding.conjugate_sign, ComplexShape.associative_ε₂_eq_mul, eq_pow_of_mul_eq_pow_odd_right, sq_of_gcd_eq_one, associated_iff, CochainComplex.HomComplex.Cochain.rightShift_leftShift, IsCyclotomicExtension.Rat.discr, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom, HNNExtension.NormalWord.unitsSMulGroup_snd, HNNExtension.NormalWord.unitsSMul_one_group_smul, two_pow_two_pow_add_two_pow_two_pow, Pell.Solution₁.prop_y, HomologicalComplex₂.totalAux.d₂_eq', HomologicalComplex₂.totalAux.d₁_eq, HomologicalComplex₂.D₁_totalShift₂XIso_hom_assoc, ModEq.pow_eq_pow, HomologicalComplex.mapBifunctor.d₂_eq, PadicInt.norm_int_le_pow_iff_dvd, Pell.Solution₁.prop, HomologicalComplex.ι_mapBifunctorFlipIso_inv_assoc, isUnit_iff_natAbs_eq, AlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinLM_comp_apply, List.prod_int_mod, Equiv.Perm.sign_bij, Function.Antiperiodic.add_zsmul_eq, qrSign.sq_eq_one, units_pow_eq_pow_mod_two, ComplexShape.ε₂_ε₁, Fin.sign_cycleIcc_of_le, ModEq.pow, fermatNumber_eq_fermatNumber_sq_sub_two_mul_fermatNumber_sub_one_sq, negOnePow_one, Equiv.Perm.mem_alternatingGroup, Equiv.Perm.ofSign_disjoint, Matrix.det_reindex, IsCyclotomicExtension.Rat.absdiscr_prime_pow_succ, Polynomial.coeff_hermite_explicit, Equiv.Perm.sign_of_pow_two_eq_one, Polynomial.IsUnitTrinomial.leadingCoeff_isUnit, legendreSym.sq_one', HomologicalComplex₂.D₁_totalShift₁XIso_hom_assoc, units_div_eq_mul, natCast_emultiplicity, Equiv.Perm.sign_refl, CochainComplex.HomComplex.δ_comp, PythagoreanTriple.coprime_classification', IsCyclotomicExtension.Rat.discr_prime_pow_succ, negOnePow_odd, ComplexShape.σ_ε₁, CategoryTheory.Limits.FormalCoproduct.cochainComplexFunctor_obj_d, AlgebraicTopology.AlternatingFaceMapComplex.obj_d_eq, Polynomial.Chebyshev.iterate_derivative_U_eval_one_dvd, Polynomial.Chebyshev.iterate_derivative_T_eval_one_dvd, Finset.inclusion_exclusion_card_biUnion, Polynomial.coeff_hermite_of_even_add, negOnePow_def, ComplexShape.associative_ε₁_eq_mul, Ring.choose_neg', AbsoluteValue.map_units_int_smul, HomologicalComplex₂.ιTotal_totalFlipIso_f_hom_assoc, Equiv.Perm.sign_mul, Rat.divInt_pow, two_pow_sub_pow', sq_add_sq_of_two_mul_sq_add_sq, CochainComplex.shiftFunctor_map_f, Function.Antiperiodic.zsmul_sub_eq, legendreSym.quadratic_reciprocity', Polynomial.cardPowDegree_apply, natAbs_eq_iff_sq_eq, squarefree_natAbs, Equiv.Perm.signAux3_mul_and_swap, natCast_pow_pred, HomologicalComplex₂.ι_totalShift₂Iso_hom_f_assoc, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₁, ZMod.gauss_lemma, extDerivWithin_apply_vectorField, Equiv.Perm.sign_symm_trans_trans, LaurentSeries.hasseDeriv_coeff, Equiv.Perm.mem_ofSign, ComplexShape.ε_zero, HomologicalComplex.mapBifunctor₂₃.d₁_eq, abs_negOnePow, isUnit_iff_abs_eq, coe_negOnePow, negOnePow_two_mul_add_one, Polynomial.Chebyshev.U_eval_two_mul_zero, le_self_sq, abs_unit_intCast, HomologicalComplex.eulerChar_eq_sum_finSet_of_finrankSupport_subset, numDerangements_sum, TensorProduct.CompatibleSMul.int, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f, HomologicalComplex₂.D₁_totalShift₁XIso_hom, HomologicalComplex₂.D₂_totalShift₁XIso_hom, units_eq_one_or, TotalComplexShapeSymmetry.σ_ε₂, Matrix.submatrix_succAbove_det_eq_negOnePow_submatrix_succAbove_det', nnnorm_units_zsmul, uzpow_add, units_natAbs, MultilinearMap.alternatization_apply, PythagoreanTriple.classification, LaurentSeries.hasseDeriv_single_add, ComplexShape.σ_ε₂, finiteMultiplicity_iff_finiteMultiplicity_natAbs, Equiv.Perm.decomposeOption_symm_sign, Finset.sum_powerset_neg_one_pow_card_of_nonempty, Rat.isFractionRingNum, CochainComplex.HomComplex.Cochain.δ_toSingleMk, Matrix.detp_smul_adjp, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₂, IsCyclotomicExtension.Rat.absdiscr_prime, exists_unit_of_abs, cast_npow, HNNExtension.NormalWord.empty_toList, Pell.Solution₁.prop_x, le_self_pow_two, Equiv.Perm.sign_permCongr, Matrix.detp_one_diagonal, natAbs_le_self_sq, eq_pow_of_mul_eq_pow_odd_left, Ring.multichoose_neg_of_lt, ModEq.pow_prime_eq_self, PythagoreanTriple.coprime_classification, IsCyclotomicExtension.Rat.discr_prime_pow, negOnePow_sub, one_uzpow, ArithmeticFunction.moebius_sq_eq_one_of_squarefree, ContinuousMultilinearMap.alternatization_apply_toContinuousMultilinearMap, padicValRat.multiplicity_sub_multiplicity, HNNExtension.toSubgroupEquiv_neg_apply, emultiplicity_pow_add_pow, ZMod.χ₄_eq_neg_one_pow, units_coe_mul_self, natAbs_le_iff_sq_le, Polynomial.Chebyshev.U_eval_neg, CochainComplex.HomComplex.Cochain.δ_shift, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₃, Polynomial.Chebyshev.iterate_derivative_U_eval_one, HomologicalComplex₂.totalShift₁Iso_trans_totalShift₂Iso, addSubmonoid_closure_range_pow, AlgebraicTopology.DoldKan.hσ'_eq, HomologicalComplex₂.d₂_eq, Polynomial.Chebyshev.C_eval_neg_two, HNNExtension.NormalWord.unitsSMul_neg, ZMod.natCast_smul_units, quadraticChar_sq_one, Fintype.card_units_int, Matrix.detp_smul_add_adjp, Polynomial.Chebyshev.T_eval_zero_of_even, CategoryTheory.CatCenter.app_neg_one_zpow, ComplexShape.eulerCharSignsUpNat_χ, isUnit_sq, squarefree_natCast, coe_negOnePow_natCast, CochainComplex.HomComplex.Cochain.δ_rightUnshift, negOnePow_zero, associated_iff_natAbs, Matrix.det_mul_aux, units_sq, odd_pow, Matrix.isAddUnit_detp_smul_mul_adjp, Ring.smeval_ascPochhammer_neg_add, Finset.inclusion_exclusion_sum_biUnion, Matrix.detp_mul, List.alternatingSum_reverse, nnnorm_coe_units, two_pow_sub_pow, AbsoluteValue.map_units_int, Matrix.det_permute', GradedTensorProduct.comm_coe_tmul_coe, LucasLehmer.mersenne_int_pos, CochainComplex.HomComplex.Cochain.δ_rightShift, ComplexShape.Associative.ε₂_eq_mul, HomologicalComplex₂.ι_totalShift₂Iso_inv_f, DistribSMul.toAddMonoidHom_eq_zsmulAddGroupHom, Function.Antiperiodic.nsmul_sub_eq, emultiplicity_natAbs, CochainComplex.HomComplex.Cochain.leftShift_v, Polynomial.zero_lt_negOnePow_mul_eval_of_lt_roots_of_leadingCoeff_nonneg, PadicInt.pow_p_dvd_int_iff, ZMod.gauss_lemma_aux, Matrix.submatrix_succAbove_det_eq_negOnePow_submatrix_succAbove_det, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₃, HomologicalComplex.mapBifunctorMapHomotopy.comm₁_aux, isCoprime_of_sq_sum, fib_two_mul_add_one, ComplexShape.Associative.ε₁_eq_mul, MultilinearMap.alternatization_coe, CochainComplex.HomComplex.Cochain.δ_leftUnshift, HomologicalComplex₂.ιTotal_totalFlipIso_f_hom, Polynomial.negOnePow_mul_eval_le_zero_of_le_roots_of_leadingCoeff_nonpos, AddMonoid.End.intCast_def, negOnePow_even, IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_pow_ne_two, ComplexShape.χ_next, CochainComplex.mappingCocone.δ_descCochain, HomologicalComplex.mapBifunctor.d₁_eq', extDeriv_apply_vectorField_of_pairwise_commute, uzpow_sub, TensorProduct.tmul_of_gradedMul_of_tmul, Rat.mkRat_pow, Polynomial.cardPowDegree_nonzero, Ring.smeval_ascPochhammer_succ_neg, eight_dvd_sq_sub_one_of_odd, HNNExtension.NormalWord.unitsSMulEquiv_symm_apply, CochainComplex.shiftFunctor_obj_d', ExteriorAlgebra.ιMulti_family_mul_of_disjoint, Pell.exists_iff_not_isSquare, AlgebraicTopology.DoldKan.N₂_obj_X_d, Submonoid.log_pow_int_eq_self, coe_nat_two_pow_pred, ModEq.pow_card_sub_one_eq_one, HomologicalComplex₂.totalShift₁Iso_hom_totalShift₂Iso_hom_assoc, uzpow_intCast, Equiv.Perm.sign_extendDomain, HNNExtension.toSubgroupEquiv_one, ContinuousAlternatingMap.neg_one_pow_smul_map_removeNth_add_eq_zero_of_eq, Polynomial.Chebyshev.iterate_derivative_U_eval_one_eq_div, Polynomial.Chebyshev.iterate_derivative_T_eval_one, HNNExtension.ReducedWord.map_fst_eq_and_of_prod_eq, padicValRat.defn, Polynomial.coeff_hermite, HNNExtension.NormalWord.cons_toList, HomologicalComplex.ι_mapBifunctorFlipIso_hom, Function.Antiperiodic.add_nsmul_eq, CochainComplex.mapBifunctorShift₁Iso_trans_mapBifunctorShift₂Iso, Matrix.mul_adjp_apply_ne, Matrix.det_neg_eq_smul, NumberField.sign_discr, sign_finRotate, two_pow_two_pow_sub_pow_two_pow, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₁_assoc, norm_coe_units, Equiv.Perm.IsCycle.sign, Equiv.Perm.sign_inv, map_zsmul_unit, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₃, uzpow_neg, padicValRat.finite_int_prime_iff, HomologicalComplex.mapBifunctor.d₂_eq', Equiv.Perm.IsThreeCycle.sign, IsCyclotomicExtension.Rat.associated_norm_zeta_sub_one, AlternatingMap.domDomCongr_perm, HomologicalComplex₂.ι_totalShift₂Iso_hom_f, Equiv.Perm.IsSwap.sign_eq, TensorProduct.gradedCommAux_lof_tmul, sq_mod_four_eq_one_of_odd, ZMod.eisenstein_lemma, Ring.smeval_ascPochhammer_neg_of_lt, units_ne_iff_eq_neg, CategoryTheory.NatTrans.app_units_zsmul, Equiv.Perm.sign_prodCongrRight, CochainComplex.mappingCone.δ_descCochain, isUnit_iff, Zsqrtd.isUnit_iff_norm_isUnit, AlternatingMap.uncurryFin_apply, ComplexShape.instHasNoLoopIntUp, Polynomial.Chebyshev.one_lt_negOnePow_mul_eval_T_real, Equiv.Perm.sign_eq_sign_of_equiv, prime_dvd_pow_sub_one, Fermat42.mul, HomologicalComplex₂.d₂_eq', Equiv.Perm.sign_one, Finset.sum_powerset_neg_one_pow_card, CategoryTheory.Pretriangulated.Triangle.shiftFunctor_map_hom₂, AlternatingMap.neg_one_pow_smul_map_insertNth, ComplexShape.ε₂_def, AlternatingMap.map_insertNth, Polynomial.Chebyshev.one_le_negOnePow_mul_eval_T_real, Polynomial.Chebyshev.T_eval_neg_one, prime_dvd_pow_self_sub, ContinuousAlternatingMap.neg_one_pow_smul_map_insertNth, padicValInt.of_ne_one_ne_zero, HomologicalComplex₂.d₁_eq', extDerivWithin_apply, Ring.multichoose_neg_add, Matrix.det_apply', padicValInt_dvd, Equiv.Perm.sign_prod_list_swap, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₁, sign_eq_sign, Matrix.detp_neg_one_diagonal, mul_uzpow, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₃, HomologicalComplex₂.D₁_totalShift₂XIso_hom, GradedObject.eulerChar_eq_sum_finSet_of_finrankSupport_subset, IsCyclotomicExtension.Rat.discr_prime, Equiv.Perm.sign_prodCongrLeft, HomologicalComplex.mapBifunctor₁₂.d₁_eq, HomologicalComplex₂.D₂_totalShift₂XIso_hom, Finset.indicator_biUnion_eq_sum_powerset, AddCommGroup.smul_top_eq_top_of_divisibleBy_int, ClassGroup.norm_le, norm_units_zsmul, Polynomial.IsUnitTrinomial.trailingCoeff_isUnit, Mathlib.Tactic.Ring.intCast_mul, HomologicalComplex.mapBifunctor₁₂.d₃_eq, Equiv.Perm.sign_of_cycleType', Equiv.Perm.sign_subtypeCongr, Polynomial.Chebyshev.S_eval_neg_two, HNNExtension.NormalWord.ofGroup_toList, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₁, Nat.sq_add_sq_zmodEq, jacobiSym.quadratic_reciprocity, Polynomial.negOnePow_mul_eval_lt_zero_of_lt_roots_of_leadingCoeff_nonpos, Equiv.Perm.ofSign_disjUnion, TensorProduct.gradedComm_of_tmul_of, exteriorPower.toTensorPower_apply_ιMulti, Equiv.Perm.prod_Iio_comp_eq_sign_mul_prod, Function.Antiperiodic.int_mul_sub_eq, alternatingGroup_eq_sign_ker, HomologicalComplex.mapBifunctor₁₂.d₂_eq, Polynomial.IsUnitTrinomial.irreducible_aux1, negOnePow_succ, Ring.smeval_ascPochhammer_self_neg, Equiv.optionCongr_sign, Polynomial.bernoulli_comp_neg_X, C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum, jacobiSym.sq_one', CochainComplex.HomComplex.Cochain.δ_leftShift, HomologicalComplex₂.totalAux.d₁_eq', Matrix.mul_adjp_add_detp, TotalComplexShape.ε₂_ε₁, HomologicalComplex.ι_mapBifunctorFlipIso_hom_assoc, HNNExtension.NormalWord.unitsSMulEquiv_apply, Padic.norm_int_le_pow_iff_dvd, CategoryTheory.SimplicialObject.Homotopy.ToChainHomotopy.hom_eq, CochainComplex.HomComplex.δ_zero_cochain_comp, HNNExtension.NormalWord.t_pow_smul_eq_unitsSMul, HNNExtension.ReducedWord.toList_eq_nil_of_mem_of_range, ZMod.smul_units_def, AlgebraicTopology.DoldKan.hσ'_eq', Equiv.Perm.sign_swap', Polynomial.Chebyshev.iterate_derivative_T_eval_one_eq_div, negOnePow_eq_one_iff, Equiv.Perm.sign_swap, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₁, HomologicalComplex.mapBifunctor.d₁_eq, cast_negOnePow_natCast, HomologicalComplex.homologyEulerChar_eq_sum_finSet_of_finrankSupport_subset, fib_add_sq_sub_fib_mul_fib_add_two_mul, HomologicalComplex.mapBifunctorMapHomotopy.ιMapBifunctor_hom₂_assoc, Equiv.Perm.sign_ofSubtype, ContinuousAlternatingMap.alternatizeUncurryFin_apply, List.alternatingProd_reverse, Matrix.isAddUnit_detp_mul_detp, LaurentSeries.hasseDeriv_single, CochainComplex.shiftFunctor_obj_d, eq_pow_of_mul_eq_pow_odd, HNNExtension.ReducedWord.exists_normalWord_prod_eq, IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_ne_two, MultilinearMap.alternatization_def, CategoryTheory.ObjectProperty.smul_mem_trW_iff, multiplicity_natAbs, extDeriv_apply, IsCyclotomicExtension.Rat.discr_prime_pow_eq_unit_mul_pow', Squarefree.moebius_eq, Polynomial.Chebyshev.U_eval_zero_of_even, Polynomial.Chebyshev.eval_T_real_cos_int_mul_pi_div, HomologicalComplex.ι_mapBifunctorFlipIso_inv, Equiv.Perm.signAux_mul, associated_natAbs, Equiv.Perm.sign_surjective, Function.Antiperiodic.sub_nsmul_eq, legendreSym.quadratic_reciprocity, List.alternatingSum_eq_finset_sum, units_mul_self, Equiv.Perm.OnCycleFactors.sign_kerParam_apply_apply, Function.Antiperiodic.sub_zsmul_eq, ofMul_uzpow, HomologicalComplex₂.ιTotal_totalFlipIso_f_inv
instSemigroup 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
instIsAddTorsionFree 📖	mathematical	—	IsAddTorsionFree SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup instAddCommGroup	—	—
nsmul_eq_mul 📖	mathematical	—	AddMonoid.toNSMul instAddMonoid	—	—
zsmul_eq_mul 📖	mathematical	—	SubNegMonoid.toZSMul AddGroup.toSubNegMonoid instAddGroup	—	—

(root)

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
zsmul_int_int 📖	mathematical	—	SubNegMonoid.toZSMul AddGroup.toSubNegMonoid Int.instAddGroup	—	—
zsmul_int_one 📖	mathematical	—	SubNegMonoid.toZSMul AddGroup.toSubNegMonoid Int.instAddGroup	—	mul_one

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