Documentation Verification Report

Additive

📁 Source: Mathlib/CategoryTheory/Adjunction/Additive.lean

Statistics

MetricCount
DefinitionsAdditive, compPreadditiveYonedaIso, homAddEquiv, Additive
4
TheoremscompPreadditiveYonedaIso_hom_app_app_apply, compPreadditiveYonedaIso_inv_app_app_apply, homAddEquiv_add, homAddEquiv_apply, homAddEquiv_neg, homAddEquiv_sub, homAddEquiv_symm_add, homAddEquiv_symm_apply, homAddEquiv_symm_neg, homAddEquiv_symm_sub, homAddEquiv_symm_zero, homAddEquiv_zero, left_adjoint_additive, right_adjoint_additive
14
Total18

CategoryTheory.Adjunction

Definitions

NameCategoryTheorems
compPreadditiveYonedaIso 📖CompOp
2 mathmath: compPreadditiveYonedaIso_inv_app_app_apply, compPreadditiveYonedaIso_hom_app_app_apply
homAddEquiv 📖CompOp
2 mathmath: homAddEquiv_symm_apply, homAddEquiv_apply

Theorems

NameKindAssumesProvesValidatesDepends On
compPreadditiveYonedaIso_hom_app_app_apply 📖mathematicalDFunLike.coe
CategoryTheory.Functor.obj
Opposite
CategoryTheory.Category.opposite
AddCommGrpCat
AddCommGrpCat.instCategory
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.comp
CategoryTheory.preadditiveYoneda
CategoryTheory.Functor.whiskeringRight
AddCommGrpCat.uliftFunctor
CategoryTheory.Functor.whiskeringLeft
CategoryTheory.Functor.op
AddCommGrpCat.carrier
CategoryTheory.ConcreteCategory.hom
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddCommGrpCat.str
AddMonoidHom.instFunLike
AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier
CategoryTheory.NatTrans.app
CategoryTheory.Iso.hom
compPreadditiveYonedaIso
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
Opposite.unop
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
homEquiv
AddEquiv
ULift.add
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
CategoryTheory.Preadditive.homGroup
AddEquiv.instEquivLike
AddEquiv.ulift
compPreadditiveYonedaIso_inv_app_app_apply 📖mathematicalDFunLike.coe
CategoryTheory.Functor.obj
Opposite
CategoryTheory.Category.opposite
AddCommGrpCat
AddCommGrpCat.instCategory
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.comp
CategoryTheory.preadditiveYoneda
CategoryTheory.Functor.whiskeringLeft
CategoryTheory.Functor.op
CategoryTheory.Functor.whiskeringRight
AddCommGrpCat.uliftFunctor
AddCommGrpCat.carrier
CategoryTheory.ConcreteCategory.hom
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddCommGrpCat.str
AddMonoidHom.instFunLike
AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier
CategoryTheory.NatTrans.app
CategoryTheory.Iso.inv
compPreadditiveYonedaIso
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
Opposite.unop
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
homEquiv
AddEquiv
ULift.add
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
CategoryTheory.Preadditive.homGroup
AddEquiv.instEquivLike
AddEquiv.ulift
homAddEquiv_add 📖mathematicalDFunLike.coe
Equiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
EquivLike.toFunLike
Equiv.instEquivLike
homEquiv
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
CategoryTheory.Preadditive.homGroup
map_add
AddMonoidHomClass.toAddHomClass
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
homAddEquiv_apply 📖mathematicalDFunLike.coe
AddEquiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
CategoryTheory.Preadditive.homGroup
EquivLike.toFunLike
AddEquiv.instEquivLike
homAddEquiv
Equiv
Equiv.instEquivLike
homEquiv
homAddEquiv_neg 📖mathematicalDFunLike.coe
Equiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
EquivLike.toFunLike
Equiv.instEquivLike
homEquiv
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
CategoryTheory.Preadditive.homGroup
map_neg
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
homAddEquiv_sub 📖mathematicalDFunLike.coe
Equiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
EquivLike.toFunLike
Equiv.instEquivLike
homEquiv
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
CategoryTheory.Preadditive.homGroup
map_sub
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
homAddEquiv_symm_add 📖mathematicalDFunLike.coe
Equiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
homEquiv
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
CategoryTheory.Preadditive.homGroup
map_add
AddMonoidHomClass.toAddHomClass
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
homAddEquiv_symm_apply 📖mathematicalDFunLike.coe
AddEquiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
CategoryTheory.Preadditive.homGroup
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquiv.symm
homAddEquiv
Equiv
Equiv.instEquivLike
Equiv.symm
homEquiv
homAddEquiv_symm_neg 📖mathematicalDFunLike.coe
Equiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
homEquiv
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
CategoryTheory.Preadditive.homGroup
map_neg
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
homAddEquiv_symm_sub 📖mathematicalDFunLike.coe
Equiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
homEquiv
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
CategoryTheory.Preadditive.homGroup
map_sub
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
homAddEquiv_symm_zero 📖mathematicalDFunLike.coe
Equiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
homEquiv
CategoryTheory.Limits.HasZeroMorphisms.zero
CategoryTheory.Preadditive.preadditiveHasZeroMorphisms
map_zero
AddMonoidHomClass.toZeroHomClass
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
homAddEquiv_zero 📖mathematicalDFunLike.coe
Equiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
EquivLike.toFunLike
Equiv.instEquivLike
homEquiv
CategoryTheory.Limits.HasZeroMorphisms.zero
CategoryTheory.Preadditive.preadditiveHasZeroMorphisms
map_zero
AddMonoidHomClass.toZeroHomClass
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
left_adjoint_additive 📖mathematicalCategoryTheory.Functor.AdditiveEquiv.injective
homEquiv_unit
unit_naturality
CategoryTheory.Preadditive.add_comp
CategoryTheory.Functor.map_add
CategoryTheory.Preadditive.comp_add
right_adjoint_additive 📖mathematicalCategoryTheory.Functor.AdditiveEquiv.injective
homEquiv_counit
counit_naturality
CategoryTheory.Preadditive.comp_add
CategoryTheory.Functor.map_add
CategoryTheory.Preadditive.add_comp

CategoryTheory.Functor

Definitions

NameCategoryTheorems
Additive 📖CompData
117 mathmath: PresheafOfModules.instAdditiveRestrictScalars, CategoryTheory.linearCoyoneda_obj_additive, CategoryTheory.additive_yonedaObj, CategoryTheory.Idempotents.KaroubiKaroubi.equivalence.additive_inverse, CategoryTheory.instAdditiveObjFunctorAdditiveFunctor, SheafOfModules.instAdditiveRestrictScalars, AlgebraicGeometry.Scheme.Modules.instAdditivePullback, CategoryTheory.Quotient.functor_additive, fullSubcategoryInclusion_additive, CategoryTheory.instAdditiveObjFunctorAdditiveFunctor_1, CategoryTheory.instAdditiveHomotopyCategoryMapHomotopyCategory, additive_of_comp_faithful, map_homogical_complex_additive, CategoryTheory.Localization.instAdditiveLocalization'Q', HomotopyCategory.instAdditiveHomologicalComplexQuotientHomotopicFunctor, AlgebraicGeometry.instAdditiveModuleCatCarrierModulesSpecOfFunctor, ModuleCat.instAdditiveLocalizationLocalizedModule_functor, CategoryTheory.Localization.instAdditiveLocalizationQ, CategoryTheory.tensorLeft_additive, CategoryTheory.Idempotents.toKaroubiEquivalence_functor_additive, CategoryTheory.AsSmall.instAdditiveDown, HomotopyCategory.instAdditiveIntUpShiftFunctor, CategoryTheory.ObjectProperty.instAdditiveFullSubcategoryShiftFunctor, AddCommGrpCat.uliftFunctor_additive, CategoryTheory.ShortComplex.leftHomologyFunctor_additive, CategoryTheory.ShortComplex.rightHomologyFunctor_additive, unop_additive, CochainComplex.instAdditiveIntFunctorSingleFunctors, CategoryTheory.additive_yonedaObj', SheafOfModules.instAdditiveSheafAddCommGrpCatToSheaf, Rep.instAdditiveModuleCatObjFunctorCoinvariantsTensor, CategoryTheory.tensorRight_additive, CategoryTheory.ShortComplex.opcyclesFunctor_additive, CategoryTheory.Localization.functor_additive_iff, DerivedCategory.instAdditiveHomotopyCategoryIntUpQh, ContinuousCohomology.instAdditiveActionTopModuleCatInvariants, Action.res_additive, SemiNormedGrp.instAdditiveCompletion, CategoryTheory.Abelian.instAdditiveAddCommGrpCatExtFunctorObj, CategoryTheory.Idempotents.instAdditiveKaroubiToKaroubi, HomologicalComplex.instAdditiveHomologyFunctor, CategoryTheory.Mat_.Embedding.instAdditiveEmbedding, FGModuleCat.instAdditiveModuleCatForget₂LinearMapIdCarrierObjIsFG, HomotopyCategory.instAdditiveIntUpSingleFunctor, mapAction_preadditive, CategoryTheory.additive_coyonedaObj', CategoryTheory.ShrinkHoms.instAdditiveInverse, CochainComplex.instAdditiveIntShiftFunctor, DerivedCategory.instAdditiveShiftFunctorInt, CategoryTheory.instAdditivePullbackShiftShiftFunctorOfCoeAddMonoidHom, Action.forget_additive, additive_of_preserves_binary_products, leftOp_additive, CategoryTheory.Adjunction.right_adjoint_additive, ComplexShape.Embedding.instAdditiveHomologicalComplexRestrictionFunctor, CategoryTheory.Algebra.forget_additive, CategoryTheory.tensoringLeft_additive, CategoryTheory.ShortComplex.cyclesFunctor_additive, ModuleCat.instAdditiveRestrictScalars, PresheafOfModules.instAdditiveModuleCatCarrierObjOppositeRingCatEvaluation, ModuleCat.instAdditiveUliftFunctor, CategoryTheory.Mat_.lift_additive, CategoryTheory.Abelian.instAdditiveOppositeFunctorAddCommGrpCatExtFunctor, CategoryTheory.linearYoneda_obj_additive, CategoryTheory.Free.lift_additive, FullyFaithful.additive_ofFullyFaithful, CategoryTheory.presheafToSheaf_additive, ModuleCat.restrictScalarsEquivalenceOfRingEquiv_additive, MoritaEquivalence.instAdditiveModuleCatFunctorEqv, additive_of_iso, CategoryTheory.Monad.forget_additive, ComplexShape.Embedding.instAdditiveHomologicalComplexExtendFunctor, CategoryTheory.Equivalence.inverse_additive, groupCohomology.instAdditiveRepCochainComplexModuleCatNatCochainsFunctor, ModuleCat.forget₂_addCommGrp_additive, instAdditiveFullSubcategoryLift, instAdditiveObjEvaluation, DerivedCategory.instAdditiveCochainComplexIntQ, CategoryTheory.Comonad.forget_additive, DerivedCategory.instAdditiveSingleFunctor, CategoryTheory.Coalgebra.forget_additive, CategoryTheory.Idempotents.KaroubiKaroubi.instAdditiveKaroubiInverse, rightOp_additive, CategoryTheory.AsSmall.instAdditiveUp, instAdditiveComp, HomotopyCategory.instAdditiveHomologyFunctor, CategoryTheory.Idempotents.KaroubiKaroubi.equivalence.additive_functor, HomotopyCategory.instAdditiveHomologicalComplexQuotient, CategoryTheory.instAdditiveAdditiveFunctorFunctorForget, HomologicalComplex.instAdditiveSingle, HomologicalComplex.opFunctor_additive, HomologicalComplex.eval_additive, CategoryTheory.additive_coyonedaObj, CategoryTheory.Localization.functor_additive, Action.functorCategoryEquivalence_additive, Rep.instAdditiveModuleCatInvariantsFunctor, CategoryTheory.tensoringRight_additive, additive_of_full_essSurj_comp, op_additive, inducedFunctor_additive, HomologicalComplex.unopFunctor_additive, PresheafOfModules.instAdditiveFunctorOppositeAbToPresheaf, CategoryTheory.instAdditiveOppositeShiftShiftFunctor, AlgebraicGeometry.Scheme.Modules.instAdditivePushforward, Rep.instAdditiveModuleCatCoinvariantsFunctor, CategoryTheory.additiveFunctor_iff, CategoryTheory.Adjunction.left_adjoint_additive, SheafOfModules.instAdditivePresheafOfModulesValRingCatForget, additive_of_preservesBinaryBiproducts, ContinuousCohomology.instAdditiveActionTopModuleCatI, Action.forget₂_additive, instAdditiveFunctorColim, CategoryTheory.ShortComplex.homologyFunctor_additive, CategoryTheory.Equivalence.additive_inverse_of_FullyFaithful, CochainComplex.instAdditiveHomologicalComplexIntUpShiftFunctor, instAdditiveId, CategoryTheory.ShrinkHoms.instAdditiveFunctor

(root)

Definitions

NameCategoryTheorems
Additive 📖CompOp
315 mathmath: nndist_ofMul, Additive.instNontrivial, nhds_ofMul, NumberField.Units.logEmbedding_fundSystem, MonoidHom.toAdditive_apply_apply, Additive.ofMul_eq_top, Additive.ofMul_bot, NumberField.Units.fun_eq_repr, AddEquiv.piAdditive_apply, Additive.existsAddOfLe, AddMonoidHom.toMultiplicativeRight_apply_apply, AddAutAdditive_apply_symm_apply, isAddRightRegular_ofMul, Submonoid.fg_iff_add_fg, AddSubgroup.mem_toSubgroup', ComplexShape.eulerCharSignsDownNat_χ, toMul_uzpow, even_ofMul_iff, isSquare_toMul_iff, MulEquiv.toAdditive_apply_apply, AddEquiv.toMultiplicativeRight_apply_apply, AddEquiv.additiveMultiplicative_apply, Additive.toMul_symm_eq, Additive.vaddCommClass, toMul_ofMul, uzpow_natCast, toMul_neg, AddChar.directSum_apply, AddAction.stabilizer_vadd_eq_stabilizer_map_conj, groupCohomology.isMulCoboundary₁_of_mem_coboundaries₁, WeierstrassCurve.Affine.Point.toClass_zero, groupCohomology.mem_cocycles₁_of_addMonoidHom, norm_ofMul, Additive.ofMul_top, ofMul_list_prod, AddAutAdditive_apply_apply, AddMonoidHom.coe_toMultiplicativeRight, nnnorm_toMul, AddAutAdditive_symm_apply_symm_apply, uzpow_coe_nat, nndist_toMul, Additive.toMul_le, MonoidHom.toAdditive_symm_apply_apply, groupCohomology.H1IsoOfIsTrivial_inv_apply, AddSubsemigroup.toSubsemigroup'_closure, groupCohomology.cocycles₁IsoOfIsTrivial_hom_hom_apply_apply, uniformContinuous_toMul, AddEquiv.toMultiplicativeLeft_apply_symm_apply, ComplexShape.ε_down_ℕ, AddMonCat.equivalence_inverse_map, groupCohomology.isMulCoboundary₂_of_mem_coboundaries₂, AddMonCat.equivalence_counitIso, Submonoid.toAddSubmonoid_closure, Additive.isIsIsometricVAdd, uniformContinuous_ofMul, ofMul_multiset_prod, Order.pred_toMul, AddAut.conj_symm_apply, NumberField.Units.span_basisOfIsMaxRank, AddEquiv.toMultiplicativeRight_apply_symm_apply, instInfiniteAdditive, NumberField.Units.logEmbeddingQuot_apply, Cardinal.mk_additive, NumberField.Units.basisOfIsMaxRank_apply, AddMonoidHom.toMultiplicativeRight_symm_apply_apply, instProperSpaceAdditive, groupCohomology.H1IsoOfIsTrivial_H1π_apply_apply, instCompactSpaceAdditive, isLeftRegular_toMul, groupCohomology.isMulCocycle₁_of_mem_cocycles₁, ofMul_vadd, AddEquiv.toAdditive_toMultiplicative_symm_apply, NumberField.Units.instFiniteIntAdditiveUnitsRingOfIntegers, Subgroup.fg_iff_add_fg, Additive.isCancelAdd, ofMul_zpow, GrpCat.toAddGrp_map, ofMul_pow, Additive.isLeftCancelAdd, ofMul_inv, Order.succ_ofMul, monoidEndToAdditive_apply_apply, addOrderOf_ofMul_eq_orderOf, Fintype.card_additive, AddMonoidHom.coe_toMultiplicativeLeft, Additive.instTwoUniqueSumsOfTwoUniqueProds, MonoidHom.toAdditiveLeft_apply_apply, Rep.toAdditive_symm_apply, AddChar.coe_toAddMonoidHom, NumberField.Units.fundSystem_mk, Additive.instUniqueSumsOfUniqueProds, toMul_zero, exists_prime_addEquiv_ZMod, NumberField.Units.dirichletUnitTheorem.map_logEmbedding_sup_torsion, Pi.single_additiveOfMul_eq, Rep.ofMulDistribMulAction_ρ_apply_apply, toMul_add, toMul_sum, isClosedMap_ofMul, NumberField.InfinitePlace.ComplexEmbedding.conjugate_sign, Representation.norm_ofMulDistribMulAction_eq, NumberField.Units.rank_modTorsion, isAddCyclic_additive, Valuation.ofAddValuation_apply, toMul_sub, AddAction.stabilizerEquivStabilizer_symm_apply, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow', Subsemigroup.toAddSubsemigroup_closure, NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component, MonoidHom.coe_toAdditive_map, AddMonoid.fg_of_monoid_fg, GroupFG.iff_add_fg, ofMul_image_powers_eq_multiples_ofMul, Valuation.toAddValuation_apply, AddMonCat.equivalence_inverse_obj_coe, Additive.toMul_lt, Subgroup.coe_toAddSubgroup_symm_apply, ofMul_image_zpowers_eq_zmultiples_ofMul, Additive.isOrderedCancelAddMonoid, AddAut.conj_inv_apply, AddChar.coe_toAddMonoidHomEquiv, instContinuousAddAdditiveOfContinuousMul, Additive.isIsIsometricVAdd', AddEquiv.toMultiplicativeLeft_symm_apply_symm_apply, Additive.ofMul_strictMono, groupCohomology.norm_ofAlgebraAutOnUnits_eq, Additive.ofMul_mono, instDenselyOrderedAdditive, MulEquiv.toMultiplicative_toAdditive_symm_apply, AddChar.toAddMonoidHomEquiv_symm_zero, groupCohomology.isMulCocycle₂_of_mem_cocycles₂, Rep.toAdditive_apply, instIsAddKleinFourAdditiveOfIsKleinFour, NumberField.mixedEmbedding.logMap_eq_logEmbedding, AddEquiv.toMultiplicativeRight_symm_apply_apply, edist_toMul, AddEquiv.piAdditive_symm_apply, toMul_zsmul, Additive.isRightCancelAdd, groupHomology.H1AddEquivOfIsTrivial_single, instDiscreteTopologyAdditive, instIsSuccArchimedeanAdditive, AddMonoidHom.coe_toMultiplicative', instNoncompactSpaceAdditive, Additive.ofMul_le, Valuation.ofAddValuation_toAddValuation, instFiniteAdditive, Int.negOnePow_def, MulEquiv.multiplicativeAdditive_apply, Additive.toMul_bot, AddChar.toAddMonoidHomEquiv_symm_apply, Monoid.fg_iff_add_fg, AddAction.IsBlock.of_addSubgroup_of_conjugate, AddMonoid.exponent_additive, MonoidHom.coe_toAdditiveLeft, instIsTopologicalAddGroupAdditiveOfIsTopologicalGroup, AddEquiv.prodAdditive_apply, Additive.ext_iff, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow, NumberField.Units.dirichletUnitTheorem.logEmbedding_eq_zero_iff, Additive.canonicallyOrderedAdd, groupCohomology.cocycles₁IsoOfIsTrivial_inv_hom_apply_coe, Additive.instArchimedean, AddCommMonCat.equivalence_inverse_obj_coe, AddEquiv.prodAdditive_symm_apply, groupCohomology.cocyclesOfIsMulCocycle₂_coe, Valuation.toAddValuation_symm_eq, Subgroup.toAddSubgroup_closure, MonoidHom.toAdditiveRight_symm_apply_apply, isRightRegular_toMul, AddMonoidHom.toMultiplicativeLeft_symm_apply_apply, groupCohomology.coboundariesOfIsMulCoboundary₁_coe, instLocallyCompactSpaceAdditive, Subgroup.coe_toAddSubgroup_apply, monoidEndToAdditive_symm_apply_apply, groupHomology.H1AddEquivOfIsTrivial_symm_apply, AddEquiv.toMultiplicativeRight_symm_apply_symm_apply, groupHomology.H1ToTensorOfIsTrivial_H1π_single, Order.succ_toMul, MulEquiv.toAdditive_symm_apply_apply, Subgroup.index_toAddSubgroup, MulEquiv.multiplicativeAdditive_symm_apply, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_apply, ofMul_one, groupCohomology.cocyclesOfIsMulCocycle₁_coe, AddAction.toPermHom_apply_symm_apply, AddAut.conj_apply, NumberField.mixedEmbedding.logMap_unit_smul, Additive.toMul_top, dist_toMul, isOfFinAddOrder_ofMul_iff, toMul_nsmul, MonoidHom.coe_toAdditive_range, MonoidHom.toAdditive_id, MulEquiv.toMultiplicative_toAdditive_apply, WeierstrassCurve.Affine.Point.toClass_some, continuous_ofMul, isOpenMap_ofMul, Additive.ofMul_eq_bot, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpow', ZMod.natCast_smul_units, instLipschitzAddAdditiveOfLipschitzMul, WeierstrassCurve.Affine.Point.toClass_injective, Additive.forall, isAddRegular_ofMul, instSubsingletonAdditive, groupHomology.H1AddEquivOfIsTrivial_apply, ComplexShape.eulerCharSignsUpNat_χ, MonoidHom.coe_toAdditive, Subsemigroup.coe_toAddSubsemigroup_symm_apply, NumberField.Units.dirichletUnitTheorem.logEmbedding_component, Additive.ofMul_lt, toMul_smul, NumberField.Units.logEmbeddingQuot_injective, AddEquiv.additiveMultiplicative_symm_apply, nnnorm_ofMul, Subgroup.toAddSubgroup_comap, instTotallyDisconnectedSpaceAdditive, ofMul_mul, instIsPredArchimedeanAdditive, AddChar.toAddMonoidHom_apply, AddAction.stabilizerEquivStabilizer_apply, MulEquiv.toAdditive_symm_apply_symm_apply, edist_ofMul, denselyOrdered_additive_iff, AddEquiv.toAdditive_toMultiplicative_apply, MulEquiv.toAdditive_apply_symm_apply, instWeaklyLocallyCompactSpaceAdditive, isAddLeftRegular_ofMul, toMul_eq_one, instBoundedSpaceAdditive, ofMul_prod, toMul_multiset_sum, Submonoid.coe_toAddSubmonoid_symm_apply, Submonoid.coe_toAddSubmonoid_apply, uzpow_intCast, Additive.toMul_eq_bot, AddAction.toPermHom_apply_apply, GrpCat.toAddGrp_obj_coe, AddChar.toAddMonoidHomEquiv_zero, AddSubgroup.toSubgroup'_closure, AddAction.coe_toPermHom, AddCommMonCat.equivalence_counitIso, NumberField.Units.logEmbeddingEquiv_apply, AddEquiv.toMultiplicativeLeft_symm_apply_apply, Additive.isIsIsometricVAdd'', Circle.expHom_apply, AddMonoidHom.toMultiplicativeLeft_apply_apply, toMul_list_sum, isRegular_toMul, norm_toMul, groupHomology.mkH1OfIsTrivial_apply, Representation.ofMulDistribMulAction_apply_apply, isAddCyclic_additive_iff, IsPrimitiveRoot.zmodEquivZPowers_apply_coe_nat, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom, ofMul_toMul, WeierstrassCurve.Affine.Point.toClass_eq_zero, Order.pred_ofMul, MonoidHom.coe_toAdditiveRight, instIsAddTorsionFreeAdditiveOfIsMulTorsionFree, Additive.exists, isClosedMap_toMul, MulEquiv.Monoid.End_apply, FreeAbelianGroup.liftAddEquiv_apply_apply, MonoidHom.toAdditiveLeft_symm_apply_apply, Valuation.toValuation_ofValuation, NumberField.Units.instFiniteIntAdditiveQuotientUnitsRingOfIntegersSubgroupTorsion, dist_ofMul, AddCommMonCat.equivalence_inverse_map, MonoidHom.coe_toAdditive'', AddChar.toAddMonoidHomEquiv_apply, CommGrpCat.toAddCommGrp_obj_coe, Multiplicative.monoidHom_ext_iff, NumberField.Units.regulator_eq_det', continuous_toMul, NumberField.Units.dirichletUnitTheorem.logEmbedding_ker, AddAut.neg_conj_apply, MonoidHom.coe_toMultiplicative, AddMonoidHom.coe_toMultiplicative'', Additive.addMonoidHom_ext_iff, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, Additive.addAction_isPretransitive, IsPrimitiveRoot.zmodEquivZPowers_apply_coe_int, NumberField.Units.regOfFamily_eq_det', AddSubgroup.coe_toSubgroup_symm_apply, AddGroup.fg_of_group_fg, MonoidHom.toAdditiveRight_apply_apply, ZMod.smul_units_def, ofMul_eq_zero, AddAutAdditive_symm_apply_apply, Valuation.ofAddValuation_symm_eq, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_assoc, Additive.toMul_eq_top, WeierstrassCurve.Affine.Point.toClass_apply, CommGrpCat.toAddCommGrp_map, Additive.foMul_strictMono, Additive.ofMul_symm_eq, AddSubmonoid.toSubmonoid'_closure, MonoidHom.coe_toAdditive', MonoidHom.coe_toAdditive_ker, Additive.mem_toAddSubgroup, AddEquiv.toMultiplicativeLeft_apply_apply, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpow, NumberField.Units.instFreeIntAdditiveQuotientUnitsRingOfIntegersSubgroupTorsion, nhds_toMul, instContinuousNegAdditiveOfContinuousInv, Subgroup.relIndex_toAddSubgroup, Subsemigroup.coe_toAddSubsemigroup_apply, isOpenMap_toMul, AddChar.coe_toAddMonoidHomEquiv_symm, ofMul_uzpow, Additive.isOrderedAddMonoid, uniformity_additive, ofMul_div

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