| Name | Category | Theorems |
|---|
CompatibleSMul 📖 | CompData | 6 mathmath: IsLocalization.instCompatibleSMulLocalizationOfIsScalarTower_1, CompatibleSMul.int, Algebra.TensorProduct.instCompatibleSMulRat, CompatibleSMul.isScalarTower, IsLocalization.tensorProduct_compatibleSMul, CompatibleSMul.unit
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Eqv 📖 | CompData | 1 mathmath: CharacterModule.homEquiv_apply_apply
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add 📖 | CompOp | 27 mathmath: Matrix.kroneckerTMulStarAlgEquiv_symm_apply, Algebra.Generators.H1Cotangent.δAux_mul, smul_add, MatrixEquivTensor.invFun_add, KaehlerDifferential.mulActionBaseChange_smul_add, PolynomialLaw.toFun_add_apply, Algebra.Generators.H1Cotangent.δAux_toAlgHom, Prod.comul_apply, Matrix.kroneckerTMulStarAlgEquiv_apply, groupHomology.H1AddEquivOfIsTrivial_single, PolyEquivTensor.invFun_add, Matrix.kroneckerTMul_add, PolynomialLaw.add_def_apply, PolynomialLaw.add_def, groupHomology.H1AddEquivOfIsTrivial_symm_apply, LieModule.lie_tmul_right, add_smul, PolynomialLaw.toFun_add, Matrix.add_kroneckerTMul, groupHomology.H1AddEquivOfIsTrivial_apply, tmul_add, add_tmul, neg_add_cancel, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, Matrix.kroneckerStarAlgEquiv_apply, Matrix.kroneckerStarAlgEquiv_symm_apply, AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero
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addCommMonoid 📖 | CompOp | 1217 mathmath: Pi.comul_eq_adjoint, finsuppRight_apply, DFinsupp.comul_single, SemimoduleCat.MonoidalCategory.triangle, mapInclIsometry_apply, LinearMap.lTensor_ker_subtype_tensorKerEquiv_symm, KaehlerDifferential.kerCotangentToTensor_toCotangent, CliffordAlgebra.toBaseChange_reverse, congr_symm, forall_vanishesTrivially_iff_forall_fg_rTensor_injective, Submodule.rTensorOne_symm_apply, Bialgebra.comul_natCast, lTensor.inverse_comp_lTensor, LinearMap.baseChange_eq_ltensor, Module.Flat.iff_lTensor_exact', enorm_lid, Submodule.FG.rTensor.directedSystem, Matrix.toLin_kronecker, AlternatingMap.domCoprod.summand_mk'', Coalgebra.lTensor_counit_comul, Matrix.kroneckerTMulStarAlgEquiv_symm_apply, Algebra.Presentation.differentials.comm₁₂_single, LinearEquiv.lTensor_pow, Rep.MonoidalClosed.linearHomEquiv_symm_hom, GradedTensorProduct.hom_ext_iff, Module.Basis.tensorProduct_apply, AlgebraTensorModule.rid_symm_apply, Module.FaithfullyFlat.iff_exact_iff_lTensor_exact, IsGroupLikeElem.comul_eq_tmul_self, MvPolynomial.rTensor_apply_tmul_apply, PiTensorProduct.tmulEquiv_symm_apply, AlgebraTensorModule.tensorTensorTensorComm_symm, LinearMap.baseChange_smul, Algebra.Generators.H1Cotangent.δAux_mul, AlgCat.hom_inv_associator, LinearMap.convMul_def, Submodule.mulMap_tmul, Submodule.comm_trans_lTensorOne, MvPolynomial.scalarRTensor_apply_monomial_tmul, LinearMap.lTensor_sub, LaurentPolynomial.comul_T, Submodule.exists_fg_le_eq_rTensor_inclusion, finsuppTensorFinsupp_apply, range_mapIncl, congr_congr, LinearMap.rTensor_comm, LinearMap.BilinMap.baseChange_isSymm, equivFinsuppOfBasisLeft_symm_apply, Submodule.tensorEquivSpan_apply_tmul, LinearMap.baseChange_comp, LinearEquiv.coe_baseChange, Algebra.Extension.H1Cotangent.equiv_apply, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul', Algebra.Generators.cotangentSpaceBasis_apply, AlgebraTensorModule.congr_refl, Module.FaithfullyFlat.lTensor_injective_iff_injective, kroneckerTMulAlgEquiv_symm_single_tmul, Module.Flat.iff_rTensor_preserves_injective_linearMap, LieAlgebra.LoopAlgebra.twoCochainOfBilinear_apply_apply, AddMonoidAlgebra.comul_single, LinearMap.tensorKer_tmul, AlgebraTensorModule.map_id, LinearMap.lTensor_rTensor_comp_assoc, Module.rankAtStalk_eq, sum_tmul_basis_right_injective, Pi.comul_comp_dFinsuppCoeFnLinearMap, Submodule.mulMap_one_right_eq, piScalarRight_symm_algebraMap, AlgebraTensorModule.congr_symm, enorm_comm, LinearMap.rTensor_smul_action, AlgebraTensorModule.rid_tmul, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul, Coalgebra.sum_map_tmul_counit_eq, Algebra.IsPushout.cancelBaseChange_tmul, span_tmul_eq_top, tensorTensorTensorComm_tmul, gradedComm_tmul_one, AlgebraTensorModule.congr_symm_tmul, Algebra.Presentation.differentials.comm₂₃, Coalgebra.sum_tmul_counit_eq, QuotSMulTop.equivTensorQuot_naturality, Module.Flat.lTensor_preserves_injective_linearMap, Module.Flat.ker_lTensor_eq, KaehlerDifferential.cotangentComplexBaseChange_tmul, tensorTensorTensorComm_comp_map, Module.Invertible.instTensorProduct_1, range_map, CoalgCat.MonoidalCategoryAux.associator_hom_toLinearMap, Coalgebra.coassoc_symm_apply, LinearMap.tensorEqLocusEquiv_apply, lTensor.inverse_of_rightInverse_comp_lTensor, LinearMap.baseChange_baseChange, Algebra.TensorProduct.tensorTensorTensorComm_symm, TensorPower.gMul_eq_coe_linearMap, map_injective_of_flat_flat_of_isDomain, LinearMap.lTensor_id_apply, map_comp_comm_eq, Algebra.Extension.formallySmooth_iff_split_injection, InnerProductSpace.canonicalCovariantTensor_eq_sum, Module.Flat.lTensor_exact, Module.FaithfullyFlat.lTensor_exact_iff_exact, AlternatingMap.domCoprod_coe, AdicCompletion.ofTensorProduct_surjective_of_finite, MvPolynomial.scalarRTensor_apply_X_tmul_apply, ext_iff_inner_right_threefold', map_add_right, Module.FaithfullyFlat.lTensor_bijective_iff_bijective, Algebra.FormallyUnramified.finite_of_free_aux, rTensor_injective_iff_lcomp_surjective, gradedMul_assoc, contractLeft_assoc_coevaluation, Matrix.kroneckerTMul_assoc', Submodule.FG.lTensor.directedSystem, LinearMap.rTensor_id, CommRing.Pic.mul_eq_tensor, AlgebraTensorModule.rightComm_symm_tmul, LinearMap.tensorKer_coe, Module.rank_baseChange, map_map, Algebra.Extension.CotangentSpace.map_id, Algebra.IsPushout.cancelBaseChange_symm_tmul, IsLocalization.instIsLocalizedModuleTensorProductMap, Algebra.TensorProduct.piRightHom_mul, Submodule.val_mulMap'_tmul, quotTensorEquivQuotSMul_comp_mkQ_rTensor, LinearMap.lTensor_smul, directSum_lof_tmul_lof, KaehlerDifferential.kerToTensor_apply, AlgebraTensorModule.lTensor_comp_cancelBaseChange, AlgebraTensorModule.lTensor_id, quotientTensorQuotientEquiv_symm_apply_mk_tmul, Pi.comul_comp_single, zero_prodMap_dualTensorHom, LinearMap.mul'_comp_comm, AlgebraTensorModule.rTensor_one, Algebra.TensorProduct.basis_apply, LinearMap.lTensor_surj_iff_rTensor_surj, LinearMap.liftBaseChange_one_tmul, LinearMap.rTensor_id_apply, AlgHom.mulLeftRightMatrix.inv_comp, LinearEquiv.rTensor_mul, le_comap_range_lTensor, BialgCat.associator_def, QuotSMulTop.equivTensorQuot_naturality_mk, Module.endTensorEndAlgHom_apply, tensorIteratedFDerivTwo_eq_iteratedFDeriv, coe_directSumRight', finsuppTensorFinsupp'_symm_single_eq_tmul_single_one, PolynomialLaw.exists_lift', LinearMap.toMatrix_baseChange, Coalgebra.sum_counit_tmul_eq, SemimoduleCat.hom_inv_rightUnitor, PolynomialLaw.toFun_eq_rTensor_φ_toFun', LinearIsometryEquiv.lTensor_apply, dualDistrib_dualDistribInvOfBasis_right_inverse, LinearMap.rTensor_comp_lTensor, Algebra.Extension.lTensor_cotangentComplex_eq_cotangentComplexBaseChange, LinearMap.rTensor_comp_map, LinearMap.rTensor_comp_flip_mk, dualDistrib_apply_comm, CharacterModule.curry_apply_apply, LinearEquiv.coe_lTensor, Algebra.TensorProduct.assoc_tmul, map₂_eq_range_lift_comp_mapIncl, Module.FaithfullyFlat.iff_zero_iff_rTensor_zero, directLimitRight_tmul_of, flip_mk_surjective, LinearMap.rTensor_tmul, exists_finite_submodule_of_finite', tensorQuotEquivQuotSMul_comp_mkQ_lTensor, Algebra.Generators.liftBaseChange_injective_of_isLocalizationAway, equivFinsuppOfBasisLeft_apply_tmul_apply, CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_right, leftComm_tmul, Orthonormal.basisTensorProduct, comm_comm, QuadraticForm.tmul_tensorMap_apply, Submodule.mulMap_comm, Module.Flat.out, map_injective_of_flat_flat', Algebra.Generators.cotangentSpaceBasis_repr_one_tmul, AlgebraTensorModule.map_smul_left, Algebra.TensorProduct.leftComm_tmul, gradedMul_def, rTensor.inverse_of_rightInverse_apply, KaehlerDifferential.instIsScalarTowerTensorProduct, ModuleCat.MonoidalCategory.associator_hom_apply, AlgebraTensorModule.restrictScalars_lTensor, Finsupp.linearCombination_one_tmul, Module.FaithfullyFlat.lTensor_surjective_iff_surjective, AlgebraTensorModule.restrictScalars_curry, LinearMap.trace_eq_contract_of_basis', Submodule.linearDisjoint_iff, QuadraticForm.tmul_comp_tensorComm, LinearEquiv.comm_trans_lTensor_trans_comm_eq, GradedTensorProduct.auxEquiv_one, Algebra.TensorProduct.basis_repr_tmul, CoalgHom.map_comp_comul, toMatrix_assoc, Bialgebra.TensorProduct.comul_eq_algHom_toLinearMap, Module.FaithfullyFlat.zero_iff_rTensor_zero, LinearMap.lTensor_comp_comm, Polynomial.X_pow_smul_rTensor_monomial, Algebra.TensorProduct.linearEquivIncludeRange_toLinearMap, retractionOfSectionOfKerSqZero_comp_kerToTensor, LinearMap.coe_lTensorHom, KaehlerDifferential.mapBaseChange_tmul, ModuleCat.ExtendRestrictScalarsAdj.Counit.map_hom_apply, LinearMap.baseChange_one, Bialgebra.TensorProduct.map_toCoalgHom, Algebra.Generators.H1Cotangent.δAux_C, gradedComm_algebraMap_tmul, LinearMap.BilinMap.tmul_isSymm, finsuppLeft_smul', Algebra.FormallySmooth.iff_injective_cotangentComplexBaseChange_residueField, Algebra.Extension.subsingleton_h1Cotangent, Coalgebra.sum_map_tmul_tmul_eq, Algebra.TensorProduct.basisAux_map_smul, Pi.intrinsicStar_comul_commSemiring, equivFinsuppOfBasisRight_apply_tmul, congr_zpow, Algebra.Extension.CotangentSpace.map_tmul, LinearMap.lTensor_range, Coalgebra.comm_comul, LocalizedModule.equivTensorProduct_symm_apply_tmul_one, Rep.ihom_ev_app_hom, CommRing.Pic.mk_tensor, LocalizedModule.equivTensorProduct_apply_mk, Module.Flat.iff_lTensor_preserves_injective_linearMap, lTensor.inverse_of_rightInverse_apply, equivFinsuppOfBasisLeft_apply_tmul, QuadraticForm.polarBilin_tmul, lidIsometry_apply, LinearEquiv.lTensor_zpow, Algebra.Extension.H1Cotangent.val_zero, Algebra.TensorProduct.tensorTensorTensorComm_symm_tmul, isGroupLikeElem_iff, LinearMap.tensorKerEquivOfSurjective_symm_tmul, equivFinsuppOfBasisLeft_symm, comm_trans_lid, LinearMap.tensorEqLocus_coe, tensorIteratedFDerivWithinTwo_eq_iteratedFDerivWithin, PointedCone.tmul_mem_maxTensorProduct, curry_injective, lTensorHomEquivHomLTensor_apply, finsuppScalarRight_apply, Algebra.FormallySmooth.iff_injective_lTensor_residueField, isBaseChange_tensorProduct_map, LinearMap.trace_eq_contract, LinearEquiv.rTensor_trans_congr, LocalizedModule.equivTensorProduct_symm_apply_tmul, LinearMap.rTensor_sub, finsuppScalarRight_apply_tmul, rightComm_symm, Algebra.IsEpi.injective_lift_mul, Bialgebra.TensorProduct.counit_eq_algHom_toLinearMap, Coalgebra.TensorProduct.lid_tmul, homTensorHomEquiv_apply, mk_apply, LieAlgebra.LoopAlgebra.toFinsupp_symm_single, mapOfCompatibleSMul_surjective, finsuppTensorFinsupp'_single_tmul_single, Module.Flat.iff_rTensor_injective, LinearMap.baseChange_pow, Representation.tprod_apply, dualTensorHom_apply, Algebra.exists_of_fg, QuadraticForm.tensorRId_symm_apply, Module.Invertible.tensorProductComm_eq_refl, LinearEquiv.lTensor_trans_congr, Module.Invertible.rTensorEquiv_apply_apply, lTensorHomEquivHomLTensor_toLinearMap, LinearEquiv.lTensor_tmul, Ideal.map_includeRight_eq, AlgHom.comp_mul', LinearMap.intrinsicStar_mul', exists_finite_submodule_left_of_setFinite, quotientTensorEquiv_symm_apply_mk_tmul, AlgCat.hom_hom_associator, LinearEquiv.rTensor_zpow, QuadraticForm.tensorAssoc_toLinearEquiv, AlgebraTensorModule.rTensor_tensor, LinearMap.polyCharpoly_baseChange, AlgebraTensorModule.rTensor_comp, coevaluation_apply_one, IsLocalRing.map_tensorProduct_mk_eq_top, Bialgebra.TensorProduct.comulAlgHom_def, finsuppTensorFinsuppLid_symm_single_smul, LinearMap.lTensor_surjective, congr_refl_refl, rTensorHomEquivHomRTensor_apply, LinearMap.trace_eq_contract_apply, congr_trans, dualTensorHomEquivOfBasis_symm_cancel_right, map_add_left, MvPolynomial.scalarRTensor_apply_tmul, prodLeft_tmul, tensorTensorTensorComm_symm, IsLocalization.tensorProduct_isLocalizedModule, MultilinearMap.domCoprodDep_apply, finsuppTensorFinsupp'_symm_single_mul, Submodule.surjective_tensorToSpan, LinearMap.BilinForm.tensorDistribEquiv_toLinearMap, PolyEquivTensor.toFunLinear_mul_tmul_mul, directSumRight_comp_rTensor, SemimoduleCat.hom_hom_rightUnitor, KaehlerDifferential.tensorKaehlerEquivBase_tmul, lTensor.inverse_apply, map_map_assoc_symm, Module.Invertible.bijective_curry, KaehlerDifferential.tensorKaehlerEquivBase_symm_apply, comm_symm, instDirectedSystemCoeLinearMapIdRTensor, GradedTensorProduct.auxEquiv_symm_one, GradedTensorProduct.auxEquiv_comm, finsuppLeft_symm_apply_single, LinearMap.rTensor_injective_iff_subtype, LinearMap.BilinForm.tensorDistrib_tmul, AlgebraTensorModule.mk_apply, QuadraticForm.baseChange_tmul, IsTensorProduct.equiv_symm_apply, ext_iff_inner_left_threefold', LinearIsometry.lTensor_apply, finsuppTensorFinsupp'_apply_apply, LinearMap.mul'_apply, AlgebraTensorModule.rTensor_tmul, prodLeft_symm_tmul, ext_iff_inner_left_threefold, Module.FaithfullyFlat.rTensor_exact_iff_exact, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_apply, LinearEquiv.rTensor_refl_apply, MultilinearMap.domCoprod_alternization_coe, inner_lid_lid, LinearMap.BilinForm.tensorDistribEquiv_apply, Algebra.Generators.H1Cotangent.exact_map_δ, Algebra.Generators.H1Cotangent.δAux_monomial, norm_comm, map₂_apply_tmul, Algebra.Generators.CotangentSpace.compEquiv_symm_zero, dualDistribEquivOfBasis_symm_apply, LieModule.weight_vector_multiplication, leftComm_def, Algebra.Generators.cotangentSpaceBasis_repr_tmul, LinearMap.rTensor_lTensor_comp_assoc_symm, LinearMap.liftBaseChangeEquiv_symm_apply, Finsupp.comul_comp_lapply, Algebra.TensorProduct.equivFinsuppOfBasis_apply, CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_left, gradedComm_algebraMap, map_map_comp_assoc_eq, Algebra.TensorProduct.opAlgEquiv_apply, CoalgCat.associator_def, Algebra.Extension.Hom.sub_one_tmul, LinearMap.BilinForm.IsSymm.baseChange, norm_assoc, lift.tmul', assoc_tmul, Algebra.TensorProduct.equivFinsuppOfBasis_symm_apply, QuadraticForm.tensorRId_apply, MvPolynomial.rTensor_apply_X_tmul, QuadraticForm.comp_tensorLId_eq, LinearIndepOn.tmul_of_flat_right, KaehlerDifferential.exact_mapBaseChange_map, LinearMap.tensorProductEnd_apply, ModuleCat.hom_inv_associator, Bialgebra.TensorProduct.assoc_tmul, KaehlerDifferential.tensorKaehlerEquiv_tmul, inner_mapIncl_mapIncl, LinearMap.trace_eq_contract', Algebra.Generators.H1Cotangent.δAux_toAlgHom, Matrix.kroneckerAlgEquiv_apply, exists_finite_submodule_right_of_setFinite, lTensor_exact, AlgebraTensorModule.leftComm_tmul, CoalgCat.MonoidalCategoryAux.tensorObj_comul, gradedComm_tmul_of_zero, equivFinsuppOfBasisRight_apply_tmul_apply, Module.End.rTensorAlgHom_apply_apply, Module.Flat.iff_lTensor_exact, PolynomialLaw.exists_lift, CommRing.Pic.mapAlgebra_apply, congr_tmul, Algebra.Extension.CotangentSpace.map_toInfinitesimal_bijective, HopfAlgCat.associator_def, Module.Flat.rTensor_exact, KaehlerDifferential.range_mapBaseChange, Algebra.SubmersivePresentation.sectionCotangent_eq_iff, ModuleCat.MonoidalCategory.associator_def, MultilinearMap.domCoprod_domDomCongr_sumCongr, LinearEquiv.rTensor_pow, Ideal.pi_tensorProductMk_quotient_surjective, MvPolynomial.rTensor_apply_tmul, AlgebraTensorModule.congr_mul, nnnorm_map, Module.FaithfullyFlat.iff_exact_iff_rTensor_exact, Module.Flat.iff_lTensor_preserves_injective_linearMap', LinearMap.lTensor_smul_action, transpose_dualTensorHom, AlgebraTensorModule.assoc_tmul, LinearMap.lTensor_neg, Submodule.coe_tensorSpanEquivSpan_apply_tmul, LieSubmodule.mem_baseChange_iff, LinearEquiv.baseChange_mul, Submodule.FG.lTensor.directLimit_apply', directSumLeft_tmul_lof, Algebra.Generators.H1Cotangent.exact_δ_map, Algebra.Generators.cotangentCompLocalizationAwayEquiv_symm_comp_inl, kroneckerTMulLinearEquiv_one, MultilinearMap.domCoprod_alternization_eq, AlgebraTensorModule.leftComm_symm_tmul, AlgebraTensorModule.rightComm_tmul, KaehlerDifferential.mapBaseChange_surjective, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.fromExtendScalars_hom_apply, Module.FaithfullyFlat.iff_zero_iff_lTensor_zero, AdicCompletion.coe_ofTensorProductEquivOfFiniteNoetherian, AlgebraTensorModule.assoc_symm_tmul, algebraMap_gradedMul, Submodule.FG.rTensor.directLimit_apply, directLimitLeft_rTensor_of, finsuppScalarRight_smul, lid_symm_apply, IsTensorProduct.equiv_apply, Bialgebra.comul_algebraMap, lift_compr₂ₛₗ, tensorQuotEquivQuotSMul_tmul_mk, finsuppTensorFinsupp_single, counit_tmul, Algebra.Extension.CotangentSpace.map_sub_map, lid_tmul, SemimoduleCat.hom_inv_leftUnitor, FGModuleCat.FGModuleCatCoevaluation_apply_one, LinearMap.BilinMap.baseChange_tmul, Module.Flat.eqLocus_lTensor_eq, QuadraticForm.tmul_tensorAssoc_apply, exists_finite_submodule_left_of_finite, LinearMap.intrinsicStar_rTensor, piRight_symm_apply, AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_symm_of, gradedComm_one, lift.tmul, finsuppTensorFinsupp'_symm_single_eq_single_one_tmul, lTensorHomToHomLTensor_apply, Coalgebra.sum_counit_tmul_map_eq, AlgebraTensorModule.cancelBaseChange_tmul, Module.Invertible.instTensorProduct_2, Submodule.baseChange_bot, Algebra.QuasiFinite.finite_fiber, Submodule.comm_trans_rTensorOne, Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux₂, LinearMap.smul_lTensor, intrinsicStar_map, AdicCompletion.ofTensorProduct_bijective_of_finite_of_isNoetherian, Algebra.TensorProduct.instFree, Submodule.exists_fg_le_subset_range_rTensor_subtype, rTensor_injective_of_forall_vanishesTrivially, ModuleCat.hom_hom_leftUnitor, LinearMap.map_comp_rTensor, LinearMap.IsSymm.tmul, DFinsupp.comul_comp_lapply, Module.rankAtStalk_eq_finrank_tensorProduct, finsuppScalarRight_apply_tmul_apply, SemimoduleCat.MonoidalCategory.tensorμ_apply, Algebra.TensorProduct.leftComm_toLinearEquiv, LinearEquiv.baseChange_tmul, QuadraticForm.tmul_tensorComm_apply, kroneckerLinearEquiv_symm_kronecker, finsuppLeft_apply, ModuleCat.hom_hom_rightUnitor, LinearMap.comm_comp_lTensor_comp_comm_eq, mapBilinear_apply, finsuppTensorFinsuppRid_symm_single_smul, prodRight_symm_tmul, exists_finsupp_left, gradedComm_symm, QuadraticForm.tensorLId_toLinearEquiv, AlgebraTensorModule.dualDistrib_apply, Coalgebra.IsCocomm.comm_comp_comul, Algebra.TensorProduct.toLinearEquiv_tensorTensorTensorComm, Algebra.Generators.snd_comp_cotangentCompLocalizationAwayEquiv, Module.Flat.instTensorProduct, GradedTensorProduct.auxEquiv_mul, QuadraticForm.tmul_tensorRId_apply, range_map_mono, piRight_symm_single, Submodule.lTensorOne'_tmul, rank_tensorProduct, MvPolynomial.rTensorAlgHom_toLinearMap, Submodule.rTensorOne'_tmul_one, baseChange_ext_iff, Prod.comul_apply, Rep.finsuppTensorRight_hom_hom, Algebra.Extension.CotangentSpace.map_cotangentComplex, QuotSMulTop.equivQuotTensor_naturality, Submodule.rTensorOne'_tmul, Module.Invertible.rTensor_injective_iff, Algebra.Extension.cotangentComplexBaseChange_eq_lTensor_cotangentComplex, Algebra.TensorProduct.basisAux_tmul, exists_finite_submodule_right_of_setFinite', AlgebraTensorModule.map_add_left, AlgebraTensorModule.uncurry_apply, map_comm, LinearEquiv.congr_trans_rTensor, AlternatingMap.domCoprod'_apply, Submodule.LinearDisjoint.injective, Submodule.baseChange_eq_span, tensorKaehlerQuotKerSqEquiv_symm_tmul_D, Matrix.kroneckerTMulAlgEquiv_symm_apply, AlgebraTensorModule.coe_lTensor, Coalgebra.rTensor_counit_comp_comul, Matrix.kroneckerTMulStarAlgEquiv_apply, toMatrix_dualTensorHom, LinearIndependent.tmul_of_flat_left, Algebra.Generators.H1Cotangent.δAux_ofComp, AlgebraTensorModule.homTensorHomMap_apply, Submodule.injective_tensorToSpan, CoalgCat.MonoidalCategoryAux.leftUnitor_hom_toLinearMap, AdicCompletion.ofTensorProduct_bijective_of_pi_of_fintype, Algebra.Presentation.differentials.comm₂₃', LinearMap.map_comp_lTensor, Coalgebra.TensorProduct.map_tmul, LieModule.coe_liftLie_eq_lift_coe, CoalgHomClass.map_comp_comul, SemimoduleCat.hom_inv_associator, Module.Basis.baseChange_end, lid'_apply_tmul, LinearEquiv.rTensor_refl, KaehlerDifferential.instSMulCommClassTensorProduct_1, map_smul_right, Module.Basis.baseChange_apply, LinearMap.lTensor_mul, Submodule.mulRightMap_eq_mulMap_comp, Algebra.TensorProduct.basis_repr_symm_apply', inner_assoc_assoc, kroneckerTMulLinearEquiv_mul, LinearEquiv.baseChange_zpow, kroneckerTMulLinearEquiv_symm_kroneckerTMul, ModuleCat.MonoidalCategory.tensorμ_eq_tensorTensorTensorComm, Module.Free.tensor, gradedMul_one, QuadraticForm.tensorComm_toLinearEquiv, PointedCone.tmul_subset_maxTensorProduct, KaehlerDifferential.tensorKaehlerEquiv_left_inv, QuadraticModuleCat.toIsometry_hom_leftUnitor, Submodule.rTensorOne_tmul, IsLocalizedModule.rTensor, QuadraticModuleCat.toIsometry_hom_rightUnitor, rTensor.inverse_of_rightInverse_comp_rTensor, IsBaseChange.equiv_symm_apply, congr_symm_tmul, Algebra.TensorProduct.cancelBaseChange_tmul, Submodule.coe_mulMap_comp_eq, AlgebraTensorModule.curry_apply, QuadraticForm.tensorLId_symm_apply, starLinearEquiv_tensor, Algebra.TensorProduct.mul_one, exists_finite_submodule_left_of_finite', sum_tmul, finsuppScalarRight_symm_apply_single, tmul_sum, Algebra.TensorProduct.mk_one_injective_of_isScalarTower, Module.Flat.iff_lTensor_injective, Ideal.ker_tensorProductMk_quotient, LinearEquiv.rTensor_symm_tmul, Bialgebra.comul_mul, AlgebraTensorModule.mapBilinear_apply, piRightHom_tmul, LinearMap.lTensor_comm, quotientTensorQuotientEquiv_apply_tmul_mk_tmul_mk, tensorKaehlerQuotKerSqEquiv_tmul_D, HopfAlgebra.mul_antipode_rTensor_comul, tensorQuotientEquiv_apply_mk_tmul, LinearMap.lTensor_id, exists_finite_submodule_of_finite, QuadraticForm.tensorDistrib_tmul, map_one, GradedTensorProduct.mulHom_apply, rTensor.inverse_comp_rTensor, PointedCone.minTensorProduct_le_maxTensorProduct, directSumRight_tmul_lof, Module.Invertible.rTensor_bijective_iff, MultilinearMap.domCoprod'_apply, ModuleCat.hom_inv_rightUnitor, Equiv.tensorProductAssoc_def, LinearMap.map_rTensor, QuadraticForm.tensorComm_apply, Module.Flat.linearIndependent_one_tmul, exists_multiset, Module.Flat.iff_rTensor_exact', Algebra.Generators.Cotangent.exact, kroneckerTMulLinearEquiv_tmul, LinearMap.rTensor_comp_comm, AlgebraTensorModule.restrictScalars_rTensor, QuadraticForm.tmul_comp_tensorMap, Module.Dual.baseChange_apply_tmul, LinearMap.rTensor_baseChange, Algebra.IsPushout.cancelBaseChangeAux_symm_tmul, directSumLeft_symm_lof_tmul, PointedCone.tmul_subset_minTensorProduct, rTensor_mkQ, lift_comp_map, sum_tmul_eq_zero_of_vanishesTrivially, tensorQuotEquivQuotSMul_symm_mk, Module.Flat.tensorProduct_mapIncl_injective_of_left, comm_trans_comm, QuadraticForm.tensorAssoc_symm_apply, Coalgebra.coassoc, Module.mem_freeLocus_iff_tensor, AlgebraTensorModule.map_add_right, Algebra.linearMap_comp_mul', map_injective_of_flat_flat, Module.Flat.iff_lTensor_injectiveₛ, toLinearMap_congr, LinearMap.lTensor_comp_rTensor, rid_tmul, LinearMap.lTensor_zero, Submodule.tmul_mem_baseChange_of_mem, QuadraticModuleCat.toIsometry_inv_rightUnitor, Algebra.TensorProduct.cancelBaseChange_symm_tmul, AlgebraTensorModule.map_one, PiTensorProduct.tmulEquivDep_symm_apply, Submodule.rTensorOne_tmul_one, DFinsupp.comul_comp_lsingle, LinearMap.lTensor_comp_mk, KaehlerDifferential.instSMulCommClassTensorProduct, Module.Flat.baseChange, Module.Invertible.rTensorInv_leftInverse, forall_vanishesTrivially_iff_forall_rTensor_injective, finsuppTensorFinsuppRid_single_tmul_single, IsLocalRing.split_injective_iff_lTensor_residueField_injective, LieAlgebra.LoopAlgebra.toFinsupp_single_tmul, PolynomialLaw.isCompat, Algebra.Extension.contangentEquiv_tmul, finsuppScalarLeft_apply_tmul_apply, inner_comm_comm, LinearMap.polyCharpolyAux_baseChange, LinearMap.coe_rTensorHom, Algebra.TensorProduct.assoc_toLinearEquiv, LinearMap.baseChange_sub, Coalgebra.lift_lsmul_comp_counit_comp_comul, Algebra.TensorProduct.assoc_symm_tmul, Algebra.TensorProduct.opAlgEquiv_symm_apply, Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq, map_mul, QuadraticForm.tensorRId_toLinearEquiv, groupHomology.H1AddEquivOfIsTrivial_symm_apply, PiTensorProduct.tmulEquivDep_apply, Algebra.Extension.h1Cotangentι_ext_iff, Algebra.TensorProduct.linearEquivIncludeRange_symm_tmul, LieModule.lift_apply, Algebra.Generators.toKaehler_tmul_D, isBaseChange, LaurentPolynomial.comul_C, assocIsometry_apply, Finsupp.comul_single, HopfAlgebra.mul_antipode_rTensor_comul_apply, DirectedSystem.lTensor, GradedTensorProduct.auxEquiv_tmul, KaehlerDifferential.exact_kerCotangentToTensor_mapBaseChange, AlgebraTensorModule.lTensor_comp, LinearIsometryEquiv.rTensor_apply, groupHomology.H1ToTensorOfIsTrivial_H1π_single, Algebra.Extension.H1Cotangent.val_add, homTensorHomEquiv_toLinearMap, map_bijective, KaehlerDifferential.submodule_span_range_eq_ideal, LinearMap.baseChange_neg, Bialgebra.TensorProduct.coalgebra_rid_eq_algebra_rid_apply, Module.finrank_tensorProduct, gradedComm_of_zero_tmul, Algebra.Extension.H1Cotangent.val_smul, Algebra.Presentation.differentials.comm₁₂, ModuleCat.MonoidalCategory.tensorμ_apply, IsBaseChange.endHom_apply, LinearMap.mul''_apply, Module.Invertible.rTensorInv_injective, AlgebraTensorModule.lTensor_mul, piScalarRight_symm_single, Algebra.TensorProduct.one_mul, map₂_mk_top_top_eq_top, TensorPower.gMul_def, Module.Flat.iff_rTensor_exact, LinearMap.baseChange_zero, SemimoduleCat.MonoidalCategory.associator_inv_apply, rTensor_exact, LinearMap.polyCharpolyAux_map_aeval, directSumLeft_tmul, Algebra.TensorProduct.piRightHom_one, LinearMap.liftBaseChange_tmul, Submodule.mulMap_one_left_eq, map_comp, quotTensorEquivQuotSMul_symm_mk, LinearMap.rTensor_surjective, CommAlgCat.associator_inv_hom, ModuleCat.ihom_coev_app, IsBaseChange.toDual_apply, instIsCocomm, PolyEquivTensor.toFunLinear_tmul_apply, exists_finite_submodule_of_setFinite', CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_left, DirectedSystem.rTensor, Algebra.TensorProduct.tensorTensorTensorComm_toLinearEquiv, Algebra.Generators.H1Cotangent.exact_map_δ', eq_repr_basis_left, LinearMap.lift_lsmul_mul_eq_lsmul_lift_lsmul, Module.FaithfullyFlat.zero_iff_lTensor_zero, LinearMap.lTensor_bij_iff_rTensor_bij, Submodule.mulMap_comm_of_commute, AlgebraTensorModule.map_mul, QuadraticForm.tmul_tensorLId_apply, MvPolynomial.rTensor_symm_apply_single, QuadraticForm.tensorLId_apply, ModuleCat.hom_hom_associator, IsLocalization.bijective_linearMap_mul', LinearMap.lTensor_comp_apply, LinearMap.BilinForm.tensorDistribEquiv_tmul, LinearMap.trace_tensorProduct', leftComm_symm_tmul, KaehlerDifferential.D_tensorProductTo, LinearEquiv.lTensor_refl, Algebra.Extension.toKaehler_surjective, Rep.finsuppTensorRight_inv_hom, QuotSMulTop.equivQuotTensor_naturality_mk, Submodule.mulMap_eq_mul'_comp_mapIncl, Module.Flat.iff_lTensor_preserves_injective_linearMapₛ, Module.Invertible.lTensor_injective_iff, LinearEquiv.baseChange_inv, Derivation.tensorProductTo_mul, assoc_tensor'', contractLeft_apply, Algebra.Generators.disjoint_ker_toKaehler_of_linearIndependent, LinearMap.BilinMap.tensorDistrib_tmul, LineDeriv.tensorLineDerivTwo_eq_lineDerivOp_lineDerivOp, QuadraticForm.comp_tensorRId_eq, AdicCompletion.tensor_map_id_left_eq_map, range_map_eq_span_tmul, Algebra.Generators.CotangentSpace.exact, Algebra.Generators.H1Cotangent.δAux_X, Coalgebra.sum_tmul_tmul_eq, equivFinsuppOfBasisRight_apply, Submodule.mulLeftMap_eq_mulMap_comp, counit_def, PointedCone.minTensorProduct_comm, directSum_symm_lof_tmul, LinearIndepOn.tmul_of_flat_left, Module.FaithfullyFlat.tensorProduct_mk_injective, MultilinearMap.domCoprod_apply, MonoidAlgebra.comul_single, Representation.smul_tprod_one_asModule, rTensorHomEquivHomRTensor_toLinearMap, LinearMap.lTensor_injective_of_exact_of_flat, AdicCompletion.ofTensorProduct_tmul, LieAlgebra.LoopAlgebra.residuePairing_apply_apply, LinearMap.intrinsicStar_lTensor, MvPolynomial.rTensor_apply_monomial_tmul, LinearIndependent.tmul_of_isDomain, Algebra.Generators.repr_CotangentSpaceMap, PiTensorProduct.tmulEquiv_apply, Module.Dual.baseChange_baseChange, dualDistribInvOfBasis_apply, Pi.comul_coe_finsupp, lift_mk, dualTensorHom_prodMap_zero, PolyEquivTensor.toFunLinear_one_tmul_one, LinearMap.range_liftBaseChange, enorm_assoc, NonUnitalAlgHom.comp_mul', AlgebraTensorModule.rTensor_mul, quotientTensorEquiv_apply_tmul_mk, LinearEquiv.coe_rTensor_symm, Algebra.Extension.H1Cotangent.map_apply_coe, Algebra.TensorProduct.mul_assoc, SemimoduleCat.hom_hom_associator, map_zero_left, dualDistrib_dualDistribInvOfBasis_left_inverse, Submodule.mulMap'_surjective, Algebra.Generators.toKaehler_cotangentSpaceBasis, SemimoduleCat.MonoidalCategory.leftUnitor_naturality, rightComm_tmul, exists_finsupp_right, LinearMap.rTensor_map, dualTensorHomEquivOfBasis_toLinearMap, finsuppScalarLeft_apply_tmul, directSumRight_tmul, gradedComm_tmul_algebraMap, Module.Invertible.rTensor_surjective_iff, groupHomology.H1AddEquivOfIsTrivial_apply, congr_mul, norm_lid, SemimoduleCat.MonoidalCategory.tensorμ_eq_tensorTensorTensorComm, Rep.finsuppTensorLeft_inv_hom, toLinearEquiv_assocIsometry, LinearMap.rTensor_comp, LinearMap.rTensor_zero, LinearEquiv.rTensor_trans_apply, CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_right, AlgebraTensorModule.map_smul_right, LinearEquiv.dilatransvection.baseChange, rid_symm_apply, Module.End.baseChangeHom_apply_apply, Algebra.Generators.CotangentSpace.compEquiv_symm_inr, AlgebraTensorModule.map_comp, Module.Basis.baseChange_repr_tmul, nnnorm_assoc, Matrix.kroneckerAlgEquiv_symm_apply, Coalgebra.TensorProduct.assoc_tmul, AlgebraTensorModule.lift_apply, comul_tmul, Algebra.TensorProduct.basis_repr_symm_apply, Ideal.pi_mkQ_rTensor, finsuppTensorFinsuppLid_apply_apply, Prod.comul_comp_fst, AlgebraTensorModule.tensorTensorTensorComm_symm_tmul, lcurry_apply, curry_apply, rTensor.inverse_apply, Submodule.mulMap_map_comp_eq, dualTensorHomEquivOfBasis_symm_cancel_left, map_tmul, mapIsometry_apply, Module.Invertible.rTensorEquiv_symm_apply_apply, comul_def, Module.Flat.iff_lift_lsmul_comp_subtype_injective, AlgebraTensorModule.congr_one, Coalgebra.TensorProduct.lid_toLinearEquiv, directSumRight'_restrict, AlgebraTensorModule.cancelBaseChange_symm_tmul, Submodule.FG.lTensor.directLimit_apply, lift.equiv_symm_apply, AlternatingMap.domCoprod.summand_eq_zero_of_smul_invariant, LinearMap.map_lTensor, enorm_map, Prod.comul_comp_snd, mapOfCompatibleSMul_tmul, Rep.linearization_δ_hom, Algebra.FormallySmooth.kerCotangentToTensor_injective_iff, KaehlerDifferential.derivationTensorProduct_algebraMap, Pi.comul_comp_proj, AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_apply, AlgebraTensorModule.rTensor_id, Matrix.kroneckerTMulBilinear_apply, map_map_assoc, KaehlerDifferential.tensorProductTo_surjective, Algebra.TensorProduct.linearEquivIncludeRange_symm_toLinearMap, PointedCone.maxTensorProduct_comm, Coalgebra.rTensor_counit_comul, commIsometry_apply, finsuppTensorFinsupp_symm_single, LinearMap.trace_tensorProduct, comp_dualTensorHom, Algebra.Extension.h1Cotangentι_apply, Submodule.mulMap_comp_lTensor, Coalgebra.TensorProduct.assoc_symm_tmul, Algebra.Extension.cotangentComplex_injective_iff, Algebra.TensorProduct.tensorTensorTensorComm_tmul, map_convMul_map, LinearMap.rTensor_exact_iff_lTensor_exact, gradedMul_algebraMap, Matrix.trace_kroneckerTMul, Derivation.tensorProductTo_tmul, Module.Flat.iff_rTensor_preserves_injective_linearMapₛ, homTensorHomMap_apply, Submodule.lTensorOne_symm_apply, LinearMap.tensorEqLocus_tmul, Submodule.tensorToSpan_apply_tmul, gradedCommAux_comp_gradedCommAux, QuadraticForm.tensorAssoc_apply, tensorTensorTensorComm_trans_tensorTensorTensorComm, finsuppTensorFinsuppRid_apply_apply, toLinearMap_symm_lid, LinearMap.rTensor_comp_apply, Rep.finsuppTensorLeft_hom_hom, tmul_of_gradedMul_of_tmul, Matrix.mul_kroneckerTMul_mul, LinearEquiv.coe_lTensor_symm, Submodule.lTensorOne'_one_tmul, map_dualTensorHom, exists_finite_submodule_right_of_finite, Bialgebra.comul_pow, Algebra.TensorProduct.equivPiOfFiniteBasis_symm_apply, AlgebraTensorModule.lTensor_one, finsuppRight_symm_apply_single, gradedComm_one_tmul, LinearEquiv.comm_trans_rTensor_trans_comm_eq, prodRight_tmul, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_symm_D_algebraMap, CliffordAlgebra.toBaseChange_involute, IsBaseChange.equiv_tmul, Bialgebra.comul_one, LinearMap.tensorProduct_apply, Algebra.Generators.snd_cotangentCompLocalizationAwayEquiv, finsuppTensorFinsuppLid_single_tmul_single, Submodule.exists_fg_le_subset_range_rTensor_inclusion, Algebra.tensorH1CotangentOfIsLocalization_toLinearMap, Matrix.kroneckerTMulAlgEquiv_apply, Bialgebra.TensorProduct.assoc_toCoalgEquiv, Rep.homEquiv_symm_apply_hom, ModuleCat.extendScalarsComp_hom_app_one_tmul, Module.Invertible.lTensor_surjective_iff, contractRight_apply, LinearMap.trace_eq_contract_of_basis, GradedTensorProduct.of_symm_of, Coalgebra.TensorProduct.rid_symm_apply, Algebra.Generators.CotangentSpace.map_toComp_injective, LinearMap.rTensor_range, mk_surjective, Module.End.lTensorAlgHom_apply_apply, exists_finite_submodule_right_of_finite', tensorTensorTensorAssoc_symm_tmul, finsuppLeft_apply_tmul, Module.Projective.tensorProduct, AlgebraTensorModule.map_tmul, Bialgebra.TensorProduct.lid_toCoalgEquiv, PolynomialLaw.isCompat_apply', Module.Invertible.bijective, lidOfCompatibleSMul_tmul, Module.Invertible.lTensor_bijective_iff, LineDeriv.tensorLineDerivTwo_canonicalCovariantTensor_eq_sum, Pi.comul_single, Coalgebra.coassoc_apply, Coalgebra.TensorProduct.rid_toLinearEquiv, Module.Flat.iff_flat_tensorProduct, HopfAlgebra.mul_antipode_lTensor_comul_apply, Submodule.mulMap_comp_map_inclusion, equivFinsuppOfBasisRight_symm, LinearEquiv.lTensor_trans_apply, LinearMap.liftBaseChange_comp, Submodule.lTensorOne_tmul, directLimitLeft_tmul_of, MulOpposite.comul_def, Module.Flat.iff_rTensor_injectiveₛ, Submodule.LinearDisjoint.val_mulMap_tmul, Coalgebra.coassoc_symm, Algebra.Extension.Hom.sub_tmul, lid'_symm_apply, Rep.ihom_coev_app_hom, LaurentPolynomial.comul_C_mul_T, Prod.comul_comp_inl, AlgebraTensorModule.curry_injective, LinearMap.lTensor_comp, LinearMap.rid_comp_lTensor, nnnorm_comm, Module.flat_iff, Algebra.SubmersivePresentation.sectionCotangent_comp, map_ker, Submodule.exists_fg_le_eq_rTensor_subtype, piScalarRight_apply, exists_finset, LinearEquiv.lTensor_symm_tmul, Coalgebra.lTensor_counit_comp_comul, ModuleCat.hom_inv_leftUnitor, exists_finite_submodule_of_setFinite, LinearEquiv.baseChange_pow, exists_finite_submodule_left_of_setFinite', Algebra.H1Cotangent.exact_map_δ, Coalgebra.TensorProduct.rid_tmul, Algebra.Generators.H1Cotangent.δ_comp_equiv, gradedCommAux_lof_tmul, directLimitLeft_symm_of_tmul, norm_map, CommAlgCat.associator_hom_hom, Submodule.map_range_rTensor_subtype_lid, QuadraticMap.Isometry.tmul_apply, LinearEquiv.baseChange_symm, LinearMap.mul'_tensor, PointedCone.tmul_mem_minTensorProduct, comm_tmul, dualDistrib_apply, LinearMap.lTensor_pow, Module.Invertible.instTensorProduct, HopfAlgebra.mul_antipode_lTensor_comul, Module.Basis.tensorProduct_apply', LinearMap.rTensor_neg, Pi.comul_coe_dFinsupp, PolynomialLaw.isCompat_apply, map_smul_left, congr_pow, LinearMap.lTensor_map, map_map_comp_assoc_symm_eq, tensorQuotEquivQuotSMul_comp_mk, AdicCompletion.ofTensorProduct_naturality, MvPolynomial.scalarRTensor_symm_apply_single, Representation.smul_one_tprod_asModule, equivFinsuppOfBasisLeft_apply, QuadraticModuleCat.toIsometry_inv_leftUnitor, comm_comp_comm_assoc, Algebra.Generators.cotangentCompLocalizationAwayEquiv_symm_inl, Algebra.Generators.cotangentCompLocalizationAwayEquiv_symm_inr, Coalgebra.TensorProduct.map_toLinearMap, comm_comp_comm, Submodule.baseChange_top, LinearEquiv.rTensor_trans_lTensor, SemimoduleCat.hom_hom_leftUnitor, AlgebraTensorModule.lift_tmul, Matrix.kroneckerTMul_assoc, Algebra.SubmersivePresentation.sectionCotangent_zero_of_notMem_range, LinearMap.convMul_apply, Algebra.injective_lift_lsmul, lift_compr₂, KaehlerDifferential.range_kerCotangentToTensor, LinearMap.lid_comp_rTensor, Submodule.mulMap_op, IsTensorProduct.equiv_toLinearMap, LinearIndependent.tmul_of_flat_right, Prod.comul_comp_inr, Module.Flat.tensorProduct_mapIncl_injective_of_right, lift_mk_compr₂ₛₗ, Derivation.liftKaehlerDifferential_apply, Algebra.Generators.instFreeCotangentSpaceToExtension, KaehlerDifferential.instIsScalarTowerTensorProduct_1, Finsupp.comul_comp_lsingle, MvPolynomial.rTensor_apply, ext_iff, lift_comp_comm_eq, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, vanishesTrivially_iff_sum_tmul_eq_zero, Algebra.moduleAux_apply, map_range_eq_span_tmul, IsBaseChange.linearMapLeftRightHom_apply, LinearIsometry.rTensor_apply, Module.Finite.base_change, AlgebraTensorModule.congr_trans, LinearMap.mul'_comm, CoalgHomClass.map_comp_comul_apply, Algebra.FormallySmooth.iff_injective_cotangentComplexBaseChange, Coalgebra.Repr.eq, Algebra.Generators.CotangentSpace.fst_compEquiv_apply, LinearMap.lTensor_comp_map, finsuppScalarLeft_apply, Submodule.lTensorOne_one_tmul, Algebra.FormallyUnramified.comp_sec, assoc_tensor, Submodule.baseChange_span, KaehlerDifferential.tensorKaehlerEquiv_tmul_D, quotTensorEquivQuotSMul_comp_mk, Bialgebra.TensorProduct.rid_toCoalgEquiv, PointedCone.mem_maxTensorProduct, Coalgebra.TensorProduct.assoc_toLinearEquiv, SemimoduleCat.MonoidalCategory.rightUnitor_naturality, QuadraticForm.tmul_comp_tensorAssoc, rTensorHomToHomRTensor_apply, fromDirectLimit_of_tmul, LinearMap.tensorKerEquiv_apply, Representation.dualTensorHom_comm, LinearMap.baseChange_tmul, LinearMap.transvection.baseChange, Module.Basis.tensorProduct_repr_tmul_apply, PolynomialLaw.ground_apply, LinearMap.rTensor_add, LinearEquiv.lTensor_refl_apply, star_map_apply_eq_map_intrinsicStar, Module.Invertible.rightCancelEquiv_comp_rTensor_comp_symm, one_gradedMul, AlgebraTensorModule.smul_eq_lsmul_rTensor, LinearEquiv.rTensor_trans, finsuppScalarLeft_symm_apply_single, piScalarRightHom_tmul, QuadraticForm.tensorComm_symm, Bialgebra.mul_compr₂_comul, Algebra.TensorProduct.equivPiOfFiniteBasis_apply, Algebra.SubmersivePresentation.cotangentComplex_injective, LinearMap.rTensor_pow, piRight_apply, congrIsometry_apply, LinearEquiv.baseChange_one, Equiv.tensorProductComm_def, map_pow, Module.Flat.iff_rTensor_preserves_injective_linearMap', LinearMap.rTensor_smul, toLinearMap_symm_rid, assoc_tensor', CoalgCat.MonoidalCategoryAux.rightUnitor_hom_toLinearMap, Module.Finite.tensorProduct, GradedTensorProduct.of_one, LinearEquiv.lTensor_trans_rTensor, AlgebraTensorModule.coe_rTensor, QuadraticMap.tensorDistrib_tmul, AlternatingMap.domCoprod_apply, AdicCompletion.tensor_map_id_left_injective_of_injective, Submodule.mulMap_range, nnnorm_lid, tensorQuotientEquiv_symm_apply_tmul_mk, Algebra.kerTensorProductMapIdToAlgHomEquiv_symm_apply, GradedTensorProduct.symm_of_of, matrixEquivTensor_apply, lift_mk_compr₂, LinearMap.BilinForm.baseChange_tmul, Algebra.Extension.CotangentSpace.map_comp, gradedComm_of_tmul_of, isTensorProduct, LinearMap.baseChange_mul, map_surjective, Algebra.Extension.exact_cotangentComplex_toKaehler, rank_tensorProduct', Module.Flat.iff_rTensor_injective', LinearMap.baseChange_id, MvPolynomial.scalarRTensor_apply_tmul_apply, directLimitRight_symm_of_tmul, Module.finrank_baseChange, toMatrix_comm, LinearMap.lTensor_add, dualTensorHomEquivOfBasis_apply, Submodule.FG.rTensor.directLimit_apply', Module.Flat.injective_characterModule_iff_rTensor_preserves_injective_linearMap, assoc_symm_tmul, LinearMap.ker_tensorProductMk, Algebra.Generators.CotangentSpace.map_ofComp_surjective, Matrix.kroneckerStarAlgEquiv_apply, lTensor_mkQ, LinearMap.lTensor_inj_iff_rTensor_inj, Algebra.TensorProduct.leftComm_symm_tmul, comm_symm_tmul, sum_tmul_basis_left_injective, LinearMap.comm_comp_rTensor_comp_comm_eq, equivFinsuppOfBasisRight_symm_apply, KaehlerDifferential.map_liftBaseChange_smul, Algebra.Generators.H1Cotangent.map_comp_cotangentComplex_baseChange, LinearMap.trace_baseChange, exists_sum_tmul_eq, LinearMap.lTensor_tensor, LaurentPolynomial.comul_C_mul_T_self, le_comap_range_rTensor, MultilinearMap.domCoprodDep'_apply, map_id, AlgebraTensorModule.rightComm_symm, IsBaseChange.toDualBaseChange_tmul, Coalgebra.comm_comp_comul, instDirectedSystemCoeLinearMapIdLTensor, Rep.leftRegularTensorTrivialIsoFree_hom_hom, Bialgebra.TensorProduct.assoc_symm_tmul, quotTensorEquivQuotSMul_symm_comp_mkQ, Algebra.Generators.CotangentSpace.fst_compEquiv, Algebra.Extension.CotangentSpace.map_comp_apply, Ideal.map_includeLeft_eq, gradedComm_gradedMul, Bialgebra.TensorProduct.assoc_toAlgEquiv, Algebra.Generators.H1Cotangent.equiv_apply, Algebra.Extension.CotangentSpace.map_comp_cotangentComplex, LinearEquiv.rTensor_tmul, Coalgebra.TensorProduct.lid_symm_apply, rightComm_def, finsuppRight_apply_tmul_apply, directSumRight_symm_lof_tmul, LinearEquiv.lTensor_trans, Module.Flat.iff_lTensor_injective', finsuppRight_apply_tmul, Submodule.mulMap_comp_rTensor, map_zero_right, LinearIndepOn.tmul_of_isDomain, AlgebraTensorModule.lcurry_apply, comm_trans_rid, LinearMap.baseChange_add, toMatrix_map, ext_iff_inner_right_threefold, LinearEquiv.lTensor_mul, exists_of_fg, Algebra.H1Cotangent.exact_δ_mapBaseChange, LinearMap.rTensor_mul, KaehlerDifferential.instIsScalarTowerTensorProduct_2, contractLeft_assoc_coevaluation', dualDistribEquivOfBasis_apply_apply, LinearMap.baseChangeHom_apply, Matrix.kroneckerStarAlgEquiv_symm_apply, CommSemiring.comul_apply, Algebra.Generators.H1Cotangent.δ_map, assocIsometry_symm_apply, inner_map_map, LinearMap.lTensor_tmul, LinearMap.lTensor_eqLocus_subtype_tensoreqLocusEquiv_symm, Algebra.Extension.Cotangent.map_sub_map, lid_tensor, coe_finsuppScalarRight', Algebra.FormallySmooth.iff_split_injection, Algebra.TensorProduct.mul_apply, Algebra.TensorProduct.linearEquivIncludeRange_tmul, range_mapIncl_mono, AlgebraTensorModule.congr_tmul, LinearEquiv.coe_rTensor, ModuleCat.ihom_ev_app, PolynomialLaw.isCompat', Pi.comul_comp_finsuppLcoeFun, finsuppLeft'_apply, GradedTensorProduct.of_symm_one, lift.equiv_apply, finsuppRight_tmul_single, Algebra.Extension.cotangentComplex_mk, Algebra.mul'_comp_tensorTensorTensorComm, retractionOfSectionOfKerSqZero_tmul_D, IsLocalizedModule.map_lTensor, Module.Flat.rTensor_preserves_injective_linearMap, Module.Basis.baseChange_linearMap, LinearEquiv.congr_trans_lTensor, LinearEquiv.baseChange_trans, Module.Invertible.leftCancelEquiv_comp_lTensor_comp_symm, toDirectLimit_tmul_of, AlgebraTensorModule.tensorTensorTensorComm_tmul, quotTensorEquivQuotSMul_mk_tmul, ModuleCat.MonoidalCategory.associator_inv_apply, derivationQuotKerSq_mk, uncurry_apply, tensorQuotEquivQuotSMul_symm_comp_mkQ, LinearMap.rTensor_tensor, AlgebraTensorModule.lTensor_tmul, QuadraticModuleCat.hom_hom_associator, Rep.linearization_μ_hom, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply, includeRight_lid, tensorTensorTensorAssoc_tmul, SemimoduleCat.MonoidalCategory.associator_hom_apply, finsuppLeft_apply_tmul_apply, instFinitePresentationTensorProduct, QuadraticModuleCat.hom_inv_associator, AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero, eq_repr_basis_right, kroneckerLinearEquiv_tmul, SemimoduleCat.MonoidalCategory.id_tensorHom_id, MvPolynomial.rTensorAlgHom_apply_eq
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addCommSemigroup 📖 | CompOp | — |
addMonoid 📖 | CompOp | 9 mathmath: KaehlerDifferential.instIsScalarTowerTensorProduct, finsuppLeft_smul', KaehlerDifferential.instSMulCommClassTensorProduct_1, KaehlerDifferential.instSMulCommClassTensorProduct, IsAddUnit.tmul_left, KaehlerDifferential.instIsScalarTowerTensorProduct_1, KaehlerDifferential.map_liftBaseChange_smul, KaehlerDifferential.instIsScalarTowerTensorProduct_2, IsAddUnit.tmul_right
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addSemigroup 📖 | CompOp | — |
addZeroClass 📖 | CompOp | 28 mathmath: liftAux_tmul, Algebra.TensorProduct.sMulCommClass_right, KaehlerDifferential.instIsScalarTowerTensorProduct, finsuppLeft_smul', liftAddHom_tmul, Module.Invertible.rTensorEquiv_apply_apply, Algebra.Generators.H1Cotangent.exact_map_δ, Algebra.Generators.CotangentSpace.compEquiv_symm_zero, LinearMap.tensorProductEnd_apply, Module.End.rTensorAlgHom_apply_apply, Algebra.TensorProduct.isScalarTower_right, KaehlerDifferential.instSMulCommClassTensorProduct_1, KaehlerDifferential.instSMulCommClassTensorProduct, SMul.aux_of, LinearMap.mul''_apply, Algebra.Generators.H1Cotangent.exact_map_δ', Algebra.Generators.CotangentSpace.exact, Algebra.Generators.H1Cotangent.δAux_X, Module.End.baseChangeHom_apply_apply, Algebra.Extension.tensorCotangentInvFun_smul_mk, LinearMap.tensorProduct_apply, liftAux.smul, Module.End.lTensorAlgHom_apply_apply, KaehlerDifferential.instIsScalarTowerTensorProduct_1, CharacterModule.homEquiv_apply_apply, KaehlerDifferential.map_liftBaseChange_smul, KaehlerDifferential.instIsScalarTowerTensorProduct_2, liftAux.smulₛₗ
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instDistribMulAction 📖 | CompOp | 9 mathmath: LinearMap.baseChange_smul, LinearMap.rTensor_smul_action, LinearMap.lTensor_smul, Finsupp.linearCombination_one_tmul, LinearMap.lTensor_smul_action, map_smul_right, AlgebraTensorModule.map_smul_right, map_smul_left, LinearMap.rTensor_smul
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instInhabited 📖 | CompOp | — |
instModule 📖 | CompOp | 899 mathmath: Pi.comul_eq_adjoint, finsuppRight_apply, DFinsupp.comul_single, SemimoduleCat.MonoidalCategory.triangle, mapInclIsometry_apply, LinearMap.lTensor_ker_subtype_tensorKerEquiv_symm, KaehlerDifferential.kerCotangentToTensor_toCotangent, Representation.repOfTprodIso_inv_apply, CliffordAlgebra.toBaseChange_reverse, congr_symm, forall_vanishesTrivially_iff_forall_fg_rTensor_injective, Submodule.rTensorOne_symm_apply, Bialgebra.comul_natCast, lTensor.inverse_comp_lTensor, LinearMap.baseChange_eq_ltensor, Module.Flat.iff_lTensor_exact', enorm_lid, Submodule.FG.rTensor.directedSystem, AlternatingMap.domCoprod.summand_mk'', LieModule.liftLie_apply, Coalgebra.lTensor_counit_comul, LinearEquiv.lTensor_pow, Rep.MonoidalClosed.linearHomEquiv_symm_hom, GradedTensorProduct.hom_ext_iff, Module.FaithfullyFlat.iff_exact_iff_lTensor_exact, IsGroupLikeElem.comul_eq_tmul_self, PiTensorProduct.tmulEquiv_symm_apply, LinearMap.convMul_def, Submodule.mulMap_tmul, Submodule.comm_trans_lTensorOne, MvPolynomial.scalarRTensor_apply_monomial_tmul, LinearMap.lTensor_sub, LaurentPolynomial.comul_T, Submodule.exists_fg_le_eq_rTensor_inclusion, range_mapIncl, congr_congr, Representation.repOfTprodIso_apply, LinearMap.rTensor_comm, equivFinsuppOfBasisLeft_symm_apply, Module.FaithfullyFlat.lTensor_injective_iff_injective, Rep.coindToInd_of_support_subset_orbit, Module.Flat.iff_rTensor_preserves_injective_linearMap, LieAlgebra.LoopAlgebra.twoCochainOfBilinear_apply_apply, AddMonoidAlgebra.comul_single, Representation.Coinvariants.mk_inv_tmul, LinearMap.tensorKer_tmul, LinearMap.lTensor_rTensor_comp_assoc, sum_tmul_basis_right_injective, Pi.comul_comp_dFinsuppCoeFnLinearMap, Submodule.mulMap_one_right_eq, congrIsometry_refl_refl, enorm_comm, LinearMap.rTensor_smul_action, span_tmul_eq_top, tensorTensorTensorComm_tmul, gradedComm_tmul_one, Representation.ofCoinvariantsTprodLeftRegular_mk_tmul_single, QuotSMulTop.equivTensorQuot_naturality, Module.Flat.lTensor_preserves_injective_linearMap, Module.Flat.ker_lTensor_eq, KaehlerDifferential.cotangentComplexBaseChange_tmul, tensorTensorTensorComm_comp_map, range_map, CoalgCat.MonoidalCategoryAux.associator_hom_toLinearMap, Coalgebra.coassoc_symm_apply, LinearMap.tensorEqLocusEquiv_apply, lTensor.inverse_of_rightInverse_comp_lTensor, TensorPower.gMul_eq_coe_linearMap, map_injective_of_flat_flat_of_isDomain, LinearMap.lTensor_id_apply, map_comp_comm_eq, Module.Flat.lTensor_exact, Module.FaithfullyFlat.lTensor_exact_iff_exact, AlternatingMap.domCoprod_coe, MvPolynomial.scalarRTensor_apply_X_tmul_apply, ext_iff_inner_right_threefold', map_add_right, Module.FaithfullyFlat.lTensor_bijective_iff_bijective, rTensor_injective_iff_lcomp_surjective, toLinearEquiv_lidIsometry, contractLeft_assoc_coevaluation, Matrix.kroneckerTMul_assoc', Submodule.FG.lTensor.directedSystem, LinearMap.rTensor_id, CommRing.Pic.mul_eq_tensor, LinearMap.tensorKer_coe, map_map, IsLocalization.instIsLocalizedModuleTensorProductMap, Submodule.val_mulMap'_tmul, quotTensorEquivQuotSMul_comp_mkQ_rTensor, LinearMap.lTensor_smul, KaehlerDifferential.kerToTensor_apply, AlgebraTensorModule.lTensor_comp_cancelBaseChange, AlgebraTensorModule.lTensor_id, quotientTensorQuotientEquiv_symm_apply_mk_tmul, Pi.comul_comp_single, zero_prodMap_dualTensorHom, LinearMap.mul'_comp_comm, AlgebraTensorModule.rTensor_one, LinearMap.lTensor_surj_iff_rTensor_surj, LinearMap.rTensor_id_apply, AlgHom.mulLeftRightMatrix.inv_comp, LinearEquiv.rTensor_mul, le_comap_range_lTensor, QuotSMulTop.equivTensorQuot_naturality_mk, tensorIteratedFDerivTwo_eq_iteratedFDeriv, coe_directSumRight', finsuppTensorFinsupp'_symm_single_eq_tmul_single_one, Rep.finsuppToCoinvariantsTensorFree_single, PolynomialLaw.exists_lift', SemimoduleCat.hom_inv_rightUnitor, PolynomialLaw.toFun_eq_rTensor_φ_toFun', LinearIsometryEquiv.lTensor_apply, dualDistrib_dualDistribInvOfBasis_right_inverse, LinearMap.rTensor_comp_lTensor, LinearMap.rTensor_comp_map, LinearMap.rTensor_comp_flip_mk, dualDistrib_apply_comm, Representation.Coinvariants.mk_tmul_inv, CharacterModule.curry_apply_apply, LinearEquiv.coe_lTensor, map₂_eq_range_lift_comp_mapIncl, Module.FaithfullyFlat.iff_zero_iff_rTensor_zero, directLimitRight_tmul_of, mapIsometry_id_id, flip_mk_surjective, LinearMap.rTensor_tmul, exists_finite_submodule_of_finite', tensorQuotEquivQuotSMul_comp_mkQ_lTensor, equivFinsuppOfBasisLeft_apply_tmul_apply, CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_right, leftComm_tmul, comm_comm, QuadraticForm.tmul_tensorMap_apply, Submodule.mulMap_comm, Module.Flat.out, map_injective_of_flat_flat', Algebra.TensorProduct.leftComm_tmul, gradedMul_def, rTensor.inverse_of_rightInverse_apply, AlgebraTensorModule.restrictScalars_lTensor, Finsupp.linearCombination_one_tmul, Module.FaithfullyFlat.lTensor_surjective_iff_surjective, AlgebraTensorModule.restrictScalars_curry, LinearMap.trace_eq_contract_of_basis', Submodule.linearDisjoint_iff, QuadraticForm.tmul_comp_tensorComm, LinearEquiv.comm_trans_lTensor_trans_comm_eq, GradedTensorProduct.auxEquiv_one, CoalgHom.map_comp_comul, toMatrix_assoc, Module.FaithfullyFlat.zero_iff_rTensor_zero, LinearMap.lTensor_comp_comm, Polynomial.X_pow_smul_rTensor_monomial, Algebra.TensorProduct.linearEquivIncludeRange_toLinearMap, retractionOfSectionOfKerSqZero_comp_kerToTensor, LinearMap.coe_lTensorHom, ModuleCat.ExtendRestrictScalarsAdj.Counit.map_hom_apply, gradedComm_algebraMap_tmul, Coalgebra.sum_map_tmul_tmul_eq, Algebra.TensorProduct.basisAux_map_smul, Pi.intrinsicStar_comul_commSemiring, equivFinsuppOfBasisRight_apply_tmul, congr_zpow, ModuleCat.MonoidalCategory.whiskerLeft_def, LinearMap.lTensor_range, Coalgebra.comm_comul, Rep.ihom_ev_app_hom, CommRing.Pic.mk_tensor, Module.Flat.iff_lTensor_preserves_injective_linearMap, lTensor.inverse_of_rightInverse_apply, equivFinsuppOfBasisLeft_apply_tmul, lidIsometry_apply, Module.Presentation.tensor_R, LinearEquiv.lTensor_zpow, isGroupLikeElem_iff, LinearMap.tensorKerEquivOfSurjective_symm_tmul, equivFinsuppOfBasisLeft_symm, comm_trans_lid, LinearMap.tensorEqLocus_coe, tensorIteratedFDerivWithinTwo_eq_iteratedFDerivWithin, PointedCone.tmul_mem_maxTensorProduct, curry_injective, lTensorHomEquivHomLTensor_apply, finsuppScalarRight_apply, Algebra.FormallySmooth.iff_injective_lTensor_residueField, LinearMap.trace_eq_contract, LinearEquiv.rTensor_trans_congr, LinearMap.rTensor_sub, rightComm_symm, Algebra.IsEpi.injective_lift_mul, Coalgebra.TensorProduct.lid_tmul, homTensorHomEquiv_apply, mk_apply, LieAlgebra.LoopAlgebra.toFinsupp_symm_single, mapOfCompatibleSMul_surjective, finsuppTensorFinsupp'_single_tmul_single, Module.Flat.iff_rTensor_injective, ModuleCat.MonoidalCategory.tensorHom_def, Representation.tprod_apply, dualTensorHom_apply, Algebra.exists_of_fg, QuadraticForm.tensorRId_symm_apply, Module.Invertible.tensorProductComm_eq_refl, LinearEquiv.lTensor_trans_congr, Module.Invertible.rTensorEquiv_apply_apply, lTensorHomEquivHomLTensor_toLinearMap, LinearEquiv.lTensor_tmul, Ideal.map_includeRight_eq, AlgHom.comp_mul', LinearMap.intrinsicStar_mul', exists_finite_submodule_left_of_setFinite, quotientTensorEquiv_symm_apply_mk_tmul, LinearEquiv.rTensor_zpow, QuadraticForm.tensorAssoc_toLinearEquiv, AlgebraTensorModule.rTensor_tensor, AlgebraTensorModule.rTensor_comp, coevaluation_apply_one, LieAlgebra.coe_rootSpaceWeightSpaceProduct_tmul, IsLocalRing.map_tensorProduct_mk_eq_top, Representation.coinvariantsTprodLeftRegularLEquiv_apply, finsuppTensorFinsuppLid_symm_single_smul, LinearMap.lTensor_surjective, congr_refl_refl, rTensorHomEquivHomRTensor_apply, LinearMap.trace_eq_contract_apply, congr_trans, dualTensorHomEquivOfBasis_symm_cancel_right, map_add_left, MvPolynomial.scalarRTensor_apply_tmul, tensorTensorTensorComm_symm, IsLocalization.tensorProduct_isLocalizedModule, MultilinearMap.domCoprodDep_apply, finsuppTensorFinsupp'_symm_single_mul, CoalgCat.tensorHom_def, LinearMap.BilinForm.tensorDistribEquiv_toLinearMap, PolyEquivTensor.toFunLinear_mul_tmul_mul, directSumRight_comp_rTensor, SemimoduleCat.hom_hom_rightUnitor, lTensor.inverse_apply, map_map_assoc_symm, Module.Invertible.bijective_curry, comm_symm, instDirectedSystemCoeLinearMapIdRTensor, GradedTensorProduct.auxEquiv_symm_one, GradedTensorProduct.auxEquiv_comm, LinearMap.rTensor_injective_iff_subtype, AlgebraTensorModule.mk_apply, IsTensorProduct.equiv_symm_apply, ext_iff_inner_left_threefold', RingTheory.Sequence.IsWeaklyRegular.isWeaklyRegular_lTensor, LinearIsometry.lTensor_apply, finsuppTensorFinsupp'_apply_apply, LinearMap.mul'_apply, Rep.coinvariantsTensorFreeLEquiv_apply, AlgebraTensorModule.rTensor_tmul, ext_iff_inner_left_threefold, Module.FaithfullyFlat.rTensor_exact_iff_exact, LinearEquiv.rTensor_refl_apply, MultilinearMap.domCoprod_alternization_coe, inner_lid_lid, LinearMap.BilinForm.tensorDistribEquiv_apply, norm_comm, map₂_apply_tmul, dualDistribEquivOfBasis_symm_apply, LieModule.weight_vector_multiplication, leftComm_def, LinearMap.rTensor_lTensor_comp_assoc_symm, Finsupp.comul_comp_lapply, CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_left, gradedComm_algebraMap, map_map_comp_assoc_eq, Algebra.TensorProduct.opAlgEquiv_apply, CoalgCat.associator_def, norm_assoc, lift.tmul', assoc_tmul, QuadraticForm.tensorRId_apply, QuadraticForm.comp_tensorLId_eq, LinearIndepOn.tmul_of_flat_right, LinearMap.tensorProductEnd_apply, ModuleCat.hom_inv_associator, Bialgebra.TensorProduct.assoc_tmul, inner_mapIncl_mapIncl, LinearMap.trace_eq_contract', Matrix.kroneckerAlgEquiv_apply, exists_finite_submodule_right_of_setFinite, lTensor_exact, AlgebraTensorModule.leftComm_tmul, CoalgCat.MonoidalCategoryAux.tensorObj_comul, gradedComm_tmul_of_zero, CoalgCat.comul_def, equivFinsuppOfBasisRight_apply_tmul_apply, Module.End.rTensorAlgHom_apply_apply, Module.Flat.iff_lTensor_exact, PolynomialLaw.exists_lift, ModuleCat.MonoidalCategory.rightUnitor_def, congr_tmul, Module.Flat.rTensor_exact, ModuleCat.MonoidalCategory.associator_def, MultilinearMap.domCoprod_domDomCongr_sumCongr, LinearEquiv.rTensor_pow, Ideal.pi_tensorProductMk_quotient_surjective, nnnorm_map, Module.FaithfullyFlat.iff_exact_iff_rTensor_exact, Module.Flat.iff_lTensor_preserves_injective_linearMap', LinearMap.lTensor_smul_action, transpose_dualTensorHom, Rep.indResAdjunction_counit_app_hom_hom, LinearMap.lTensor_neg, LieSubmodule.mem_baseChange_iff, Submodule.FG.lTensor.directLimit_apply', Rep.coindToInd_apply, MultilinearMap.domCoprod_alternization_eq, AlgebraTensorModule.leftComm_symm_tmul, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.fromExtendScalars_hom_apply, Module.FaithfullyFlat.iff_zero_iff_lTensor_zero, Submodule.FG.rTensor.directLimit_apply, directLimitLeft_rTensor_of, CoalgCat.whiskerRight_def, lid_symm_apply, IsTensorProduct.equiv_apply, Bialgebra.comul_algebraMap, lift_compr₂ₛₗ, tensorQuotEquivQuotSMul_tmul_mk, toLinearEquiv_congrIsometry, lid_tmul, SemimoduleCat.hom_inv_leftUnitor, Module.Flat.eqLocus_lTensor_eq, QuadraticForm.tmul_tensorAssoc_apply, exists_finite_submodule_left_of_finite, LinearMap.intrinsicStar_rTensor, gradedComm_one, toLinearEquiv_commIsometry, lift.tmul, finsuppTensorFinsupp'_symm_single_eq_single_one_tmul, lTensorHomToHomLTensor_apply, Submodule.comm_trans_rTensorOne, LinearMap.mulRight_tmul, LinearMap.smul_lTensor, intrinsicStar_map, LieModule.map_tmul, Submodule.exists_fg_le_subset_range_rTensor_subtype, rTensor_injective_of_forall_vanishesTrivially, ModuleCat.hom_hom_leftUnitor, LinearMap.map_comp_rTensor, DFinsupp.comul_comp_lapply, Algebra.TensorProduct.leftComm_toLinearEquiv, QuadraticForm.tmul_tensorComm_apply, kroneckerLinearEquiv_symm_kronecker, finsuppLeft_apply, ModuleCat.hom_hom_rightUnitor, LinearMap.comm_comp_lTensor_comp_comm_eq, mapBilinear_apply, finsuppTensorFinsuppRid_symm_single_smul, gradedComm_symm, Coalgebra.IsCocomm.comm_comp_comul, GradedTensorProduct.auxEquiv_mul, QuadraticForm.tmul_tensorRId_apply, range_map_mono, Submodule.lTensorOne'_tmul, Submodule.rTensorOne'_tmul_one, Prod.comul_apply, QuotSMulTop.equivQuotTensor_naturality, Submodule.rTensorOne'_tmul, Module.Invertible.rTensor_injective_iff, Algebra.TensorProduct.basisAux_tmul, exists_finite_submodule_right_of_setFinite', map_comm, LinearEquiv.congr_trans_rTensor, AlternatingMap.domCoprod'_apply, Submodule.LinearDisjoint.injective, Submodule.baseChange_eq_span, AlgebraTensorModule.coe_lTensor, Coalgebra.rTensor_counit_comp_comul, toMatrix_dualTensorHom, LinearIndependent.tmul_of_flat_left, CoalgCat.MonoidalCategoryAux.leftUnitor_hom_toLinearMap, LinearMap.map_comp_lTensor, LieModule.coe_liftLie_eq_lift_coe, CoalgHomClass.map_comp_comul, SemimoduleCat.hom_inv_associator, Module.Relations.Solution.IsPresentation.tensor, LinearEquiv.rTensor_refl, map_smul_right, Module.rankAtStalk_tensorProduct, LinearMap.lTensor_mul, Submodule.mulRightMap_eq_mulMap_comp, inner_assoc_assoc, ModuleCat.MonoidalCategory.tensorμ_eq_tensorTensorTensorComm, PointedCone.tmul_subset_maxTensorProduct, Submodule.rTensorOne_tmul, IsLocalizedModule.rTensor, rTensor.inverse_of_rightInverse_comp_rTensor, Module.Presentation.tensor_G, congr_symm_tmul, Submodule.coe_mulMap_comp_eq, AlgebraTensorModule.curry_apply, QuadraticForm.tensorLId_symm_apply, starLinearEquiv_tensor, Algebra.TensorProduct.mul_one, exists_finite_submodule_left_of_finite', LinearIsometryEquiv.toLinearEquiv_lTensor, Algebra.TensorProduct.mk_one_injective_of_isScalarTower, Module.Flat.iff_lTensor_injective, CliffordAlgebra.ofBaseChangeAux_ι, Ideal.ker_tensorProductMk_quotient, LinearEquiv.rTensor_symm_tmul, Bialgebra.comul_mul, AlgebraTensorModule.mapBilinear_apply, LinearMap.lTensor_comm, quotientTensorQuotientEquiv_apply_tmul_mk_tmul_mk, HopfAlgebra.mul_antipode_rTensor_comul, tensorQuotientEquiv_apply_mk_tmul, LinearMap.lTensor_id, exists_finite_submodule_of_finite, LieModule.toModuleHom_apply, map_one, GradedTensorProduct.mulHom_apply, rTensor.inverse_comp_rTensor, PointedCone.minTensorProduct_le_maxTensorProduct, directSumRight_tmul_lof, Module.Invertible.rTensor_bijective_iff, MultilinearMap.domCoprod'_apply, ModuleCat.hom_inv_rightUnitor, Equiv.tensorProductAssoc_def, LinearMap.map_rTensor, QuadraticForm.tensorComm_apply, Module.Flat.iff_rTensor_exact', LinearMap.rTensor_comp_comm, AlgebraTensorModule.restrictScalars_rTensor, QuadraticForm.tmul_comp_tensorMap, LinearMap.rTensor_baseChange, Algebra.IsPushout.cancelBaseChangeAux_symm_tmul, PointedCone.tmul_subset_minTensorProduct, rTensor_mkQ, lift_comp_map, tensorQuotEquivQuotSMul_symm_mk, Module.Relations.Solution.tensor_var, Module.Flat.tensorProduct_mapIncl_injective_of_left, comm_trans_comm, QuadraticForm.tensorAssoc_symm_apply, Coalgebra.coassoc, Algebra.linearMap_comp_mul', map_injective_of_flat_flat, Module.Flat.iff_lTensor_injectiveₛ, toLinearMap_congr, LinearMap.lTensor_comp_rTensor, rid_tmul, LinearMap.lTensor_zero, CharacterModule.homEquiv_symm_apply_apply_apply, PiTensorProduct.tmulEquivDep_symm_apply, Submodule.rTensorOne_tmul_one, DFinsupp.comul_comp_lsingle, LinearMap.lTensor_comp_mk, Module.Invertible.rTensorInv_leftInverse, forall_vanishesTrivially_iff_forall_rTensor_injective, finsuppTensorFinsuppRid_single_tmul_single, IsLocalRing.split_injective_iff_lTensor_residueField_injective, LieAlgebra.LoopAlgebra.toFinsupp_single_tmul, PolynomialLaw.isCompat, RingTheory.Sequence.IsWeaklyRegular.isWeaklyRegular_rTensor, finsuppScalarLeft_apply_tmul_apply, inner_comm_comm, LinearMap.coe_rTensorHom, Coalgebra.lift_lsmul_comp_counit_comp_comul, Algebra.TensorProduct.opAlgEquiv_symm_apply, map_mul, PiTensorProduct.tmulEquivDep_apply, Algebra.TensorProduct.linearEquivIncludeRange_symm_tmul, LieModule.lift_apply, isBaseChange, LaurentPolynomial.comul_C, assocIsometry_apply, Finsupp.comul_single, HopfAlgebra.mul_antipode_rTensor_comul_apply, DirectedSystem.lTensor, GradedTensorProduct.auxEquiv_tmul, KaehlerDifferential.exact_kerCotangentToTensor_mapBaseChange, AlgebraTensorModule.lTensor_comp, LinearIsometryEquiv.rTensor_apply, homTensorHomEquiv_toLinearMap, map_bijective, gradedComm_of_zero_tmul, Module.Invertible.rTensorInv_injective, AlgebraTensorModule.lTensor_mul, Algebra.TensorProduct.one_mul, map₂_mk_top_top_eq_top, TensorPower.gMul_def, ModuleCat.MonoidalCategory.tensorObj_isModule, Module.Flat.iff_rTensor_exact, rTensor_exact, Submodule.mulMap_one_left_eq, map_comp, quotTensorEquivQuotSMul_symm_mk, LinearMap.rTensor_surjective, ModuleCat.MonModuleEquivalenceAlgebra.inverseObj_mul, ModuleCat.ihom_coev_app, LinearIsometry.toLinearMap_rTensor, PolyEquivTensor.toFunLinear_tmul_apply, exists_finite_submodule_of_setFinite', CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_left, DirectedSystem.rTensor, LinearMap.lift_lsmul_mul_eq_lsmul_lift_lsmul, Module.FaithfullyFlat.zero_iff_lTensor_zero, LinearMap.lTensor_bij_iff_rTensor_bij, Submodule.mulMap_comm_of_commute, QuadraticForm.tmul_tensorLId_apply, QuadraticForm.tensorLId_apply, ModuleCat.hom_hom_associator, IsLocalization.bijective_linearMap_mul', LinearMap.lTensor_comp_apply, LinearIsometryEquiv.symm_rTensor, LinearMap.BilinForm.tensorDistribEquiv_tmul, LinearMap.trace_tensorProduct', commIsometry_symm, leftComm_symm_tmul, LinearEquiv.lTensor_refl, QuotSMulTop.equivQuotTensor_naturality_mk, Submodule.mulMap_eq_mul'_comp_mapIncl, Module.Flat.iff_lTensor_preserves_injective_linearMapₛ, Module.Invertible.lTensor_injective_iff, assoc_tensor'', contractLeft_apply, LineDeriv.tensorLineDerivTwo_eq_lineDerivOp_lineDerivOp, QuadraticForm.comp_tensorRId_eq, LieModule.toLinearMap_map, range_map_eq_span_tmul, Coalgebra.sum_tmul_tmul_eq, CharacterModule.dual_rTensor_conj_homEquiv, equivFinsuppOfBasisRight_apply, Submodule.mulLeftMap_eq_mulMap_comp, PointedCone.minTensorProduct_comm, LinearMap.mulLeft_tmul, Submodule.exists_fg_of_baseChange_eq_zero, LinearIndepOn.tmul_of_flat_left, CoalgCat.whiskerLeft_def, Module.FaithfullyFlat.tensorProduct_mk_injective, MultilinearMap.domCoprod_apply, MonoidAlgebra.comul_single, Representation.smul_tprod_one_asModule, rTensorHomEquivHomRTensor_toLinearMap, LinearMap.lTensor_injective_of_exact_of_flat, LieAlgebra.LoopAlgebra.residuePairing_apply_apply, LinearMap.intrinsicStar_lTensor, LinearIndependent.tmul_of_isDomain, PiTensorProduct.tmulEquiv_apply, dualDistribInvOfBasis_apply, Pi.comul_coe_finsupp, lift_mk, dualTensorHom_prodMap_zero, PolyEquivTensor.toFunLinear_one_tmul_one, MultilinearMap.domCoprod_alternization, enorm_assoc, NonUnitalAlgHom.comp_mul', AlgebraTensorModule.rTensor_mul, quotientTensorEquiv_apply_tmul_mk, LinearEquiv.coe_rTensor_symm, Algebra.TensorProduct.mul_assoc, SemimoduleCat.hom_hom_associator, map_zero_left, dualDistrib_dualDistribInvOfBasis_left_inverse, Submodule.mulMap'_surjective, SemimoduleCat.MonoidalCategory.leftUnitor_naturality, rightComm_tmul, Representation.coinvariantsTprodLeftRegularLEquiv_symm_apply, LinearMap.rTensor_map, dualTensorHomEquivOfBasis_toLinearMap, finsuppScalarLeft_apply_tmul, directSumRight_tmul, gradedComm_tmul_algebraMap, Module.Invertible.rTensor_surjective_iff, congr_mul, norm_lid, SemimoduleCat.MonoidalCategory.tensorμ_eq_tensorTensorTensorComm, toLinearEquiv_assocIsometry, LinearMap.rTensor_comp, Module.Presentation.tensor_relation, LinearMap.rTensor_zero, LinearEquiv.rTensor_trans_apply, CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_right, rid_symm_apply, Module.End.baseChangeHom_apply_apply, nnnorm_assoc, Matrix.kroneckerAlgEquiv_symm_apply, Coalgebra.TensorProduct.assoc_tmul, AlgebraTensorModule.lift_apply, Rep.leftRegularTensorTrivialIsoFree_inv_hom, comul_tmul, Ideal.pi_mkQ_rTensor, finsuppTensorFinsuppLid_apply_apply, Prod.comul_comp_fst, lcurry_apply, curry_apply, rTensor.inverse_apply, Submodule.mulMap_map_comp_eq, dualTensorHomEquivOfBasis_symm_cancel_left, map_tmul, mapIsometry_apply, Module.Invertible.rTensorEquiv_symm_apply_apply, comul_def, Module.Flat.iff_lift_lsmul_comp_subtype_injective, Coalgebra.TensorProduct.lid_toLinearEquiv, directSumRight'_restrict, Submodule.FG.lTensor.directLimit_apply, lift.equiv_symm_apply, toLinearMap_mapIsometry, AlternatingMap.domCoprod.summand_eq_zero_of_smul_invariant, LinearMap.map_lTensor, enorm_map, Prod.comul_comp_snd, mapOfCompatibleSMul_tmul, Rep.linearization_δ_hom, Algebra.FormallySmooth.kerCotangentToTensor_injective_iff, Pi.comul_comp_proj, AlgebraTensorModule.rTensor_id, Matrix.kroneckerTMulBilinear_apply, map_map_assoc, Algebra.TensorProduct.linearEquivIncludeRange_symm_toLinearMap, PointedCone.maxTensorProduct_comm, Coalgebra.rTensor_counit_comul, commIsometry_apply, LinearMap.trace_tensorProduct, comp_dualTensorHom, Submodule.mulMap_comp_lTensor, congrIsometry_symm, Coalgebra.TensorProduct.assoc_symm_tmul, map_convMul_map, LinearMap.rTensor_exact_iff_lTensor_exact, Module.Flat.iff_rTensor_preserves_injective_linearMapₛ, homTensorHomMap_apply, Submodule.lTensorOne_symm_apply, LinearMap.tensorEqLocus_tmul, QuadraticForm.tensorAssoc_apply, tensorTensorTensorComm_trans_tensorTensorTensorComm, finsuppTensorFinsuppRid_apply_apply, toLinearMap_symm_lid, LinearMap.rTensor_comp_apply, LinearEquiv.coe_lTensor_symm, Submodule.lTensorOne'_one_tmul, map_dualTensorHom, LieSubmodule.lieIdeal_oper_eq_tensor_map_range, exists_finite_submodule_right_of_finite, Bialgebra.comul_pow, AlgebraTensorModule.lTensor_one, gradedComm_one_tmul, ModuleCat.MonoidalCategory.leftUnitor_def, LinearEquiv.comm_trans_rTensor_trans_comm_eq, CliffordAlgebra.toBaseChange_involute, Bialgebra.comul_one, LinearMap.tensorProduct_apply, finsuppTensorFinsuppLid_single_tmul_single, Submodule.exists_fg_le_subset_range_rTensor_inclusion, Rep.indMap_hom, CharacterModule.uncurry_apply, Bialgebra.TensorProduct.assoc_toCoalgEquiv, Rep.homEquiv_symm_apply_hom, Module.Invertible.lTensor_surjective_iff, contractRight_apply, LinearMap.trace_eq_contract_of_basis, GradedTensorProduct.of_symm_of, LinearMap.rTensor_range, mk_surjective, Module.End.lTensorAlgHom_apply_apply, Representation.ind_mk, exists_finite_submodule_right_of_finite', tensorTensorTensorAssoc_symm_tmul, PolynomialLaw.isCompat_apply', Module.Invertible.bijective, Module.Invertible.lTensor_bijective_iff, LinearIsometryEquiv.toLinearIsometry_rTensor, LineDeriv.tensorLineDerivTwo_canonicalCovariantTensor_eq_sum, Pi.comul_single, Coalgebra.coassoc_apply, HopfAlgebra.mul_antipode_lTensor_comul_apply, Submodule.mulMap_comp_map_inclusion, equivFinsuppOfBasisRight_symm, LinearEquiv.lTensor_trans_apply, Submodule.lTensorOne_tmul, directLimitLeft_tmul_of, MulOpposite.comul_def, Module.Flat.iff_rTensor_injectiveₛ, Submodule.LinearDisjoint.val_mulMap_tmul, Coalgebra.coassoc_symm, Rep.coinvariantsTensorIndHom_mk_tmul_indVMk, Rep.ihom_coev_app_hom, LaurentPolynomial.comul_C_mul_T, Prod.comul_comp_inl, LinearMap.lTensor_comp, LinearMap.rid_comp_lTensor, nnnorm_comm, Module.flat_iff, map_ker, Submodule.exists_fg_le_eq_rTensor_subtype, LinearEquiv.lTensor_symm_tmul, Coalgebra.lTensor_counit_comp_comul, ModuleCat.hom_inv_leftUnitor, exists_finite_submodule_of_setFinite, exists_finite_submodule_left_of_setFinite', directLimitLeft_symm_of_tmul, norm_map, Submodule.map_range_rTensor_subtype_lid, QuadraticMap.Isometry.tmul_apply, LinearMap.mul'_tensor, CoalgCat.tensorObj_instCoalgebra, PointedCone.tmul_mem_minTensorProduct, comm_tmul, dualDistrib_apply, LinearMap.lTensor_pow, Module.Invertible.instTensorProduct, HopfAlgebra.mul_antipode_lTensor_comul, LinearMap.rTensor_neg, Pi.comul_coe_dFinsupp, PolynomialLaw.isCompat_apply, map_smul_left, congr_pow, LinearMap.lTensor_map, map_map_comp_assoc_symm_eq, tensorQuotEquivQuotSMul_comp_mk, MvPolynomial.scalarRTensor_symm_apply_single, CoalgCat.tensorObj_isModule, Representation.smul_one_tprod_asModule, LinearIsometryEquiv.toLinearEquiv_rTensor, equivFinsuppOfBasisLeft_apply, LinearIsometryEquiv.toLinearIsometry_lTensor, comm_comp_comm_assoc, comm_comp_comm, LinearEquiv.rTensor_trans_lTensor, SemimoduleCat.hom_hom_leftUnitor, Matrix.kroneckerTMul_assoc, LinearMap.convMul_apply, Algebra.injective_lift_lsmul, lift_compr₂, KaehlerDifferential.range_kerCotangentToTensor, LinearMap.lid_comp_rTensor, Submodule.mulMap_op, IsTensorProduct.equiv_toLinearMap, LinearIndependent.tmul_of_flat_right, Prod.comul_comp_inr, Module.Flat.tensorProduct_mapIncl_injective_of_right, lift_mk_compr₂ₛₗ, Finsupp.comul_comp_lsingle, MvPolynomial.rTensor_apply, ext_iff, lift_comp_comm_eq, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, Algebra.moduleAux_apply, map_range_eq_span_tmul, LinearIsometry.rTensor_apply, LinearMap.mul'_comm, CoalgHomClass.map_comp_comul_apply, LinearIsometry.toLinearMap_lTensor, Coalgebra.Repr.eq, LinearMap.lTensor_comp_map, finsuppScalarLeft_apply, LieModule.lieModule, Submodule.lTensorOne_one_tmul, assoc_tensor, Submodule.baseChange_span, quotTensorEquivQuotSMul_comp_mk, PointedCone.mem_maxTensorProduct, Coalgebra.TensorProduct.assoc_toLinearEquiv, SemimoduleCat.MonoidalCategory.rightUnitor_naturality, QuadraticForm.tmul_comp_tensorAssoc, rTensorHomToHomRTensor_apply, fromDirectLimit_of_tmul, LinearMap.tensorKerEquiv_apply, Representation.dualTensorHom_comm, PolynomialLaw.ground_apply, LinearMap.rTensor_add, LinearEquiv.lTensor_refl_apply, star_map_apply_eq_map_intrinsicStar, Module.Invertible.rightCancelEquiv_comp_rTensor_comp_symm, AlgebraTensorModule.smul_eq_lsmul_rTensor, LinearEquiv.rTensor_trans, finsuppScalarLeft_symm_apply_single, Bialgebra.mul_compr₂_comul, LinearMap.rTensor_pow, Representation.ind_apply, congrIsometry_apply, Equiv.tensorProductComm_def, map_pow, Module.Flat.iff_rTensor_preserves_injective_linearMap', LinearMap.rTensor_smul, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_inv_f_hom_apply, toLinearMap_symm_rid, assoc_tensor', CoalgCat.MonoidalCategoryAux.rightUnitor_hom_toLinearMap, Module.Finite.tensorProduct, GradedTensorProduct.of_one, LinearEquiv.lTensor_trans_rTensor, AlgebraTensorModule.coe_rTensor, CoalgCat.leftUnitor_def, AlternatingMap.domCoprod_apply, CharacterModule.homEquiv_apply_apply, Submodule.mulMap_range, nnnorm_lid, tensorQuotientEquiv_symm_apply_tmul_mk, GradedTensorProduct.symm_of_of, ModuleCat.MonoidalCategory.whiskerRight_def, lift_mk_compr₂, gradedComm_of_tmul_of, isTensorProduct, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, map_surjective, Module.Flat.iff_rTensor_injective', MvPolynomial.scalarRTensor_apply_tmul_apply, directLimitRight_symm_of_tmul, toMatrix_comm, LinearMap.lTensor_add, dualTensorHomEquivOfBasis_apply, Submodule.FG.rTensor.directLimit_apply', Module.Flat.injective_characterModule_iff_rTensor_preserves_injective_linearMap, assoc_symm_tmul, LinearMap.ker_tensorProductMk, Matrix.kroneckerStarAlgEquiv_apply, lTensor_mkQ, LinearMap.lTensor_inj_iff_rTensor_inj, Algebra.TensorProduct.leftComm_symm_tmul, comm_symm_tmul, sum_tmul_basis_left_injective, LinearIsometryEquiv.symm_lTensor, LinearMap.comm_comp_rTensor_comp_comm_eq, equivFinsuppOfBasisRight_symm_apply, LinearMap.lTensor_tensor, LaurentPolynomial.comul_C_mul_T_self, le_comap_range_rTensor, MultilinearMap.domCoprodDep'_apply, map_id, Coalgebra.comm_comp_comul, instDirectedSystemCoeLinearMapIdLTensor, Rep.leftRegularTensorTrivialIsoFree_hom_hom, Bialgebra.TensorProduct.assoc_symm_tmul, quotTensorEquivQuotSMul_symm_comp_mkQ, Ideal.map_includeLeft_eq, gradedComm_gradedMul, Bialgebra.TensorProduct.assoc_toAlgEquiv, LinearEquiv.rTensor_tmul, Coalgebra.TensorProduct.lid_symm_apply, rightComm_def, directSumRight_symm_lof_tmul, LinearEquiv.lTensor_trans, LieAlgebra.rootSpaceProduct_tmul, Module.Flat.iff_lTensor_injective', Submodule.mulMap_comp_rTensor, map_zero_right, LinearIndepOn.tmul_of_isDomain, comm_trans_rid, Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single, ext_iff_inner_right_threefold, LinearEquiv.lTensor_mul, exists_of_fg, LinearMap.rTensor_mul, contractLeft_assoc_coevaluation', dualDistribEquivOfBasis_apply_apply, LinearMap.baseChangeHom_apply, Matrix.kroneckerStarAlgEquiv_symm_apply, CommSemiring.comul_apply, assocIsometry_symm_apply, inner_map_map, LinearMap.lTensor_tmul, LinearMap.lTensor_eqLocus_subtype_tensoreqLocusEquiv_symm, toLinearMap_mapInclIsometry, lid_tensor, Algebra.FormallySmooth.iff_split_injection, Algebra.TensorProduct.mul_apply, lidIsometry_symm_apply, Algebra.TensorProduct.linearEquivIncludeRange_tmul, range_mapIncl_mono, LinearEquiv.coe_rTensor, ModuleCat.ihom_ev_app, Representation.IndV.hom_ext_iff, PolynomialLaw.isCompat', Pi.comul_comp_finsuppLcoeFun, GradedTensorProduct.of_symm_one, lift.equiv_apply, Rep.indResHomEquiv_symm_apply_hom, Algebra.mul'_comp_tensorTensorTensorComm, retractionOfSectionOfKerSqZero_tmul_D, IsLocalizedModule.map_lTensor, Module.Flat.rTensor_preserves_injective_linearMap, LinearEquiv.congr_trans_lTensor, Module.Invertible.leftCancelEquiv_comp_lTensor_comp_symm, toDirectLimit_tmul_of, quotTensorEquivQuotSMul_mk_tmul, uncurry_apply, tensorQuotEquivQuotSMul_symm_comp_mkQ, LinearMap.rTensor_tensor, AlgebraTensorModule.lTensor_tmul, QuadraticModuleCat.hom_hom_associator, Rep.linearization_μ_hom, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply, includeRight_lid, tensorTensorTensorAssoc_tmul, Module.Presentation.tensor_var, QuadraticModuleCat.hom_inv_associator, AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero, kroneckerLinearEquiv_tmul, SemimoduleCat.MonoidalCategory.id_tensorHom_id
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instRepr 📖 | CompOp | — |
instSMul 📖 | CompOp | 26 mathmath: IsSMulRegular.lTensor, Algebra.FormallyUnramified.finite_of_free_aux, KaehlerDifferential.isScalarTower', KaehlerDifferential.instIsScalarTowerTensorProduct, PolynomialLaw.smul_def, Ideal.map_includeRight_eq, dualDistribEquivOfBasis_symm_apply, instStarModule, algebraMap_gradedMul, Ideal.ResidueField.exists_smul_eq_tmul_one, PolynomialLaw.toFun_smul, PolynomialLaw.neg_def, dualDistribInvOfBasis_apply, smul_tmul_smul, Algebra.TensorProduct.right_isScalarTower, gradedMul_algebraMap, PolynomialLaw.smul_def_apply, PolynomialLaw.toFun_neg, liftAux.smul, IsSMulRegular.rTensor, Matrix.kroneckerStarAlgEquiv_apply, isScalarTower, Ideal.map_includeLeft_eq, Ideal.Fiber.exists_smul_eq_one_tmul, Matrix.kroneckerStarAlgEquiv_symm_apply, liftAux.smulₛₗ
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leftDistribMulAction 📖 | CompOp | 4 mathmath: AlgebraTensorModule.map_smul_left, finsuppLeft_smul', LinearMap.tensorProductEnd_apply, LinearMap.tensorProduct_apply
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leftHasSMul 📖 | CompOp | 36 mathmath: Algebra.TensorProduct.instSMulCommClassTensorProduct, Matrix.kroneckerTMulStarAlgEquiv_symm_apply, Algebra.Generators.H1Cotangent.δAux_mul, smul_add, KaehlerDifferential.cotangentComplexBaseChange_tmul, isScalarTower_right, zero_smul, Algebra.TensorProduct.sMulCommClass_right, Polynomial.X_pow_smul_rTensor_monomial, finsuppLeft_smul', Algebra.TensorProduct.basisAux_map_smul, smul_zero, tmul_smul, Algebra.TensorProduct.instSMulCommClassTensorProduct_1, tmul_eq_smul_one_tmul, Matrix.smul_kroneckerTMul, Algebra.TensorProduct.isScalarTower_right, finsuppScalarRight_smul, LinearMap.smul_lTensor, Matrix.kroneckerTMulStarAlgEquiv_apply, KaehlerDifferential.instSMulCommClassTensorProduct_1, Algebra.TensorProduct.basis_repr_symm_apply', ModuleCat.ExtendScalars.smul_tmul, KaehlerDifferential.instSMulCommClassTensorProduct, add_smul, KaehlerDifferential.submodule_span_range_eq_ideal, isScalarTower_left, smul_tmul', Algebra.Extension.tensorCotangentInvFun_smul_mk, Matrix.kroneckerTMul_smul, AlgebraTensorModule.smul_eq_lsmul_rTensor, isScalarTower, KaehlerDifferential.instIsScalarTowerTensorProduct_2, instIsCentralScalar, one_smul, smulCommClass_left
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leftModule 📖 | CompOp | 495 mathmath: finsuppRight_apply, LinearMap.lTensor_ker_subtype_tensorKerEquiv_symm, CliffordAlgebra.toBaseChange_reverse, LinearMap.baseChange_eq_ltensor, Matrix.toLin_kronecker, Matrix.kroneckerTMulStarAlgEquiv_symm_apply, Algebra.Presentation.differentials.comm₁₂_single, Module.Basis.tensorProduct_apply, AlgebraTensorModule.rid_symm_apply, MvPolynomial.rTensor_apply_tmul_apply, AlgebraTensorModule.tensorTensorTensorComm_symm, LinearMap.baseChange_smul, Algebra.Generators.H1Cotangent.δAux_mul, AlgCat.hom_inv_associator, LieSubmodule.lowerCentralSeries_tensor_eq_baseChange, finsuppTensorFinsupp_apply, LinearMap.BilinMap.baseChange_isSymm, Submodule.tensorEquivSpan_apply_tmul, LinearMap.baseChange_comp, LinearEquiv.coe_baseChange, Algebra.Extension.H1Cotangent.equiv_apply, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul', Algebra.Generators.cotangentSpaceBasis_apply, AlgebraTensorModule.congr_refl, kroneckerTMulAlgEquiv_symm_single_tmul, LinearMap.tensorKer_tmul, AlgebraTensorModule.map_id, Module.rankAtStalk_eq, piScalarRight_symm_algebraMap, AlgebraTensorModule.congr_symm, AlgebraTensorModule.rid_tmul, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul, Algebra.IsPushout.cancelBaseChange_tmul, AlgebraTensorModule.congr_symm_tmul, Algebra.Presentation.differentials.comm₂₃, Module.Flat.ker_lTensor_eq, KaehlerDifferential.cotangentComplexBaseChange_tmul, Module.Invertible.instTensorProduct_1, LinearMap.tensorEqLocusEquiv_apply, LinearMap.baseChange_baseChange, Algebra.TensorProduct.tensorTensorTensorComm_symm, Algebra.Extension.formallySmooth_iff_split_injection, AdicCompletion.ofTensorProduct_surjective_of_finite, gradedMul_assoc, AlgebraTensorModule.rightComm_symm_tmul, LinearMap.tensorKer_coe, Module.rank_baseChange, Algebra.Extension.CotangentSpace.map_id, Algebra.IsPushout.cancelBaseChange_symm_tmul, Algebra.TensorProduct.piRightHom_mul, CliffordAlgebra.equivBaseChange_symm_apply, Module.FaithfullyFlat.instTensorProduct, directSum_lof_tmul_lof, AlgebraTensorModule.lTensor_comp_cancelBaseChange, AlgebraTensorModule.lTensor_id, AlgebraTensorModule.rTensor_one, Algebra.TensorProduct.basis_apply, LinearMap.liftBaseChange_one_tmul, BialgCat.associator_def, Module.endTensorEndAlgHom_apply, coe_directSumRight', LinearMap.toMatrix_baseChange, Algebra.Extension.lTensor_cotangentComplex_eq_cotangentComplexBaseChange, Algebra.TensorProduct.assoc_tmul, Algebra.Generators.liftBaseChange_injective_of_isLocalizationAway, Orthonormal.basisTensorProduct, LinearMap.det_baseChange, QuadraticForm.tmul_tensorMap_apply, Algebra.Generators.cotangentSpaceBasis_repr_one_tmul, AlgebraTensorModule.map_smul_left, LinearEquiv.det_baseChange, gradedMul_def, AlgebraTensorModule.restrictScalars_lTensor, Finsupp.linearCombination_one_tmul, CliffordAlgebra.ofBaseChange_toBaseChange, AlgebraTensorModule.restrictScalars_curry, QuadraticForm.tmul_comp_tensorComm, QuadraticForm.polarBilin_baseChange, Algebra.TensorProduct.basis_repr_tmul, toMatrix_assoc, Bialgebra.TensorProduct.comul_eq_algHom_toLinearMap, KaehlerDifferential.mapBaseChange_tmul, ModuleCat.ExtendRestrictScalarsAdj.Counit.map_hom_apply, LinearMap.baseChange_one, Algebra.Generators.H1Cotangent.δAux_C, LinearMap.BilinMap.tmul_isSymm, finsuppLeft_smul', Algebra.FormallySmooth.iff_injective_cotangentComplexBaseChange_residueField, CliffordAlgebra.toBaseChange_comp_ofBaseChange, Algebra.Extension.subsingleton_h1Cotangent, Algebra.Extension.CotangentSpace.map_tmul, LocalizedModule.equivTensorProduct_symm_apply_tmul_one, LocalizedModule.equivTensorProduct_apply_mk, QuadraticForm.polarBilin_tmul, Algebra.Extension.H1Cotangent.val_zero, Algebra.TensorProduct.tensorTensorTensorComm_symm_tmul, LinearMap.tensorEqLocus_coe, finsuppScalarRight_apply, Algebra.FormallySmooth.iff_injective_lTensor_residueField, isBaseChange_tensorProduct_map, LocalizedModule.equivTensorProduct_symm_apply_tmul, Module.comap_freeLocus_le, CliffordAlgebra.toBaseChange_comp_involute, finsuppScalarRight_apply_tmul, Bialgebra.TensorProduct.counit_eq_algHom_toLinearMap, mapOfCompatibleSMul_surjective, LinearMap.baseChange_pow, QuadraticForm.tensorRId_symm_apply, AlgCat.hom_hom_associator, QuadraticForm.tensorAssoc_toLinearEquiv, AlgebraTensorModule.rTensor_tensor, LinearMap.polyCharpoly_baseChange, AlgebraTensorModule.rTensor_comp, Bialgebra.TensorProduct.comulAlgHom_def, prodLeft_tmul, Submodule.surjective_tensorToSpan, KaehlerDifferential.tensorKaehlerEquivBase_tmul, KaehlerDifferential.tensorKaehlerEquivBase_symm_apply, finsuppLeft_symm_apply_single, LinearMap.BilinForm.tensorDistrib_tmul, AlgebraTensorModule.mk_apply, QuadraticForm.baseChange_tmul, AlgebraTensorModule.rTensor_tmul, prodLeft_symm_tmul, Module.rankAtStalk_baseChange, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_apply, LinearMap.BilinForm.tensorDistribEquiv_apply, Algebra.Generators.H1Cotangent.exact_map_δ, Algebra.Generators.H1Cotangent.δAux_monomial, Algebra.Generators.CotangentSpace.compEquiv_symm_zero, Algebra.Generators.cotangentSpaceBasis_repr_tmul, LinearMap.liftBaseChangeEquiv_symm_apply, Algebra.TensorProduct.equivFinsuppOfBasis_apply, CoalgCat.associator_def, Algebra.Extension.Hom.sub_one_tmul, LinearMap.BilinForm.IsSymm.baseChange, Algebra.TensorProduct.equivFinsuppOfBasis_symm_apply, QuadraticForm.tensorRId_apply, MvPolynomial.rTensor_apply_X_tmul, QuadraticForm.comp_tensorLId_eq, KaehlerDifferential.exact_mapBaseChange_map, LinearMap.tensorProductEnd_apply, Bialgebra.TensorProduct.assoc_tmul, KaehlerDifferential.tensorKaehlerEquiv_tmul, Algebra.Generators.H1Cotangent.δAux_toAlgHom, AlgebraTensorModule.leftComm_tmul, CommRing.Pic.mapAlgebra_apply, Algebra.Extension.CotangentSpace.map_toInfinitesimal_bijective, HopfAlgCat.associator_def, KaehlerDifferential.range_mapBaseChange, Algebra.SubmersivePresentation.sectionCotangent_eq_iff, MvPolynomial.rTensor_apply_tmul, AlgebraTensorModule.congr_mul, AlgebraTensorModule.assoc_tmul, Submodule.coe_tensorSpanEquivSpan_apply_tmul, LieSubmodule.mem_baseChange_iff, LinearEquiv.baseChange_mul, QuadraticMap.associated_tmul, directSumLeft_tmul_lof, Algebra.Generators.H1Cotangent.exact_δ_map, Algebra.Generators.cotangentCompLocalizationAwayEquiv_symm_comp_inl, kroneckerTMulLinearEquiv_one, AlgebraTensorModule.leftComm_symm_tmul, AlgebraTensorModule.rightComm_tmul, KaehlerDifferential.mapBaseChange_surjective, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.fromExtendScalars_hom_apply, AdicCompletion.coe_ofTensorProductEquivOfFiniteNoetherian, AlgebraTensorModule.assoc_symm_tmul, algebraMap_gradedMul, finsuppScalarRight_smul, LinearMap.toMvPolynomial_baseChange, finsuppTensorFinsupp_single, counit_tmul, Algebra.Extension.CotangentSpace.map_sub_map, LinearMap.BilinMap.baseChange_tmul, Module.Flat.eqLocus_lTensor_eq, QuadraticForm.tmul_tensorAssoc_apply, piRight_symm_apply, AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_symm_of, AlgebraTensorModule.cancelBaseChange_tmul, Module.Invertible.instTensorProduct_2, Submodule.baseChange_bot, Algebra.QuasiFinite.finite_fiber, Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux₂, AdicCompletion.ofTensorProduct_bijective_of_finite_of_isNoetherian, Algebra.TensorProduct.instFree, LinearMap.IsSymm.tmul, Module.rankAtStalk_eq_finrank_tensorProduct, finsuppScalarRight_apply_tmul_apply, LinearEquiv.baseChange_tmul, QuadraticForm.tmul_tensorComm_apply, finsuppLeft_apply, prodRight_symm_tmul, QuadraticForm.tensorLId_toLinearEquiv, AlgebraTensorModule.dualDistrib_apply, Algebra.TensorProduct.toLinearEquiv_tensorTensorTensorComm, Algebra.Generators.snd_comp_cotangentCompLocalizationAwayEquiv, Module.Flat.instTensorProduct, GradedTensorProduct.auxEquiv_mul, QuadraticForm.tmul_tensorRId_apply, piRight_symm_single, rank_tensorProduct, MvPolynomial.rTensorAlgHom_toLinearMap, baseChange_ext_iff, Rep.finsuppTensorRight_hom_hom, Algebra.Extension.CotangentSpace.map_cotangentComplex, Algebra.Extension.cotangentComplexBaseChange_eq_lTensor_cotangentComplex, AlgebraTensorModule.map_add_left, AlgebraTensorModule.uncurry_apply, Submodule.baseChange_eq_span, tensorKaehlerQuotKerSqEquiv_symm_tmul_D, Matrix.kroneckerTMulAlgEquiv_symm_apply, AlgebraTensorModule.coe_lTensor, Matrix.kroneckerTMulStarAlgEquiv_apply, Algebra.Generators.H1Cotangent.δAux_ofComp, AlgebraTensorModule.homTensorHomMap_apply, Submodule.injective_tensorToSpan, AdicCompletion.ofTensorProduct_bijective_of_pi_of_fintype, Algebra.Presentation.differentials.comm₂₃', Coalgebra.TensorProduct.map_tmul, Module.Basis.baseChange_end, lid'_apply_tmul, Module.Basis.baseChange_apply, Submodule.mulRightMap_eq_mulMap_comp, Algebra.TensorProduct.basis_repr_symm_apply', kroneckerTMulLinearEquiv_mul, LinearEquiv.baseChange_zpow, kroneckerTMulLinearEquiv_symm_kroneckerTMul, Module.rankAtStalk_tensorProduct_of_isScalarTower, Module.Free.tensor, gradedMul_one, QuadraticForm.tensorComm_toLinearEquiv, CliffordAlgebra.ofBaseChange_tmul_ι, KaehlerDifferential.tensorKaehlerEquiv_left_inv, QuadraticModuleCat.toIsometry_hom_leftUnitor, IsLocalizedModule.rTensor, QuadraticModuleCat.toIsometry_hom_rightUnitor, IsBaseChange.equiv_symm_apply, Algebra.TensorProduct.cancelBaseChange_tmul, AlgebraTensorModule.curry_apply, QuadraticForm.tensorLId_symm_apply, finsuppScalarRight_symm_apply_single, CliffordAlgebra.ofBaseChangeAux_ι, AlgebraTensorModule.mapBilinear_apply, piRightHom_tmul, tensorKaehlerQuotKerSqEquiv_tmul_D, LieSubmodule.lie_baseChange, QuadraticForm.tensorDistrib_tmul, GradedTensorProduct.mulHom_apply, QuadraticForm.tensorComm_apply, Module.Flat.linearIndependent_one_tmul, Algebra.Generators.Cotangent.exact, kroneckerTMulLinearEquiv_tmul, AlgebraTensorModule.restrictScalars_rTensor, QuadraticForm.tmul_comp_tensorMap, Module.Dual.baseChange_apply_tmul, LinearMap.rTensor_baseChange, Algebra.IsPushout.cancelBaseChangeAux_symm_tmul, directSumLeft_symm_lof_tmul, QuadraticForm.tensorAssoc_symm_apply, Module.mem_freeLocus_iff_tensor, AlgebraTensorModule.map_add_right, CliffordAlgebra.toBaseChange_ofBaseChange, Submodule.tmul_mem_baseChange_of_mem, QuadraticModuleCat.toIsometry_inv_rightUnitor, Algebra.TensorProduct.cancelBaseChange_symm_tmul, AlgebraTensorModule.map_one, Module.Flat.baseChange, Algebra.Extension.contangentEquiv_tmul, LinearMap.polyCharpolyAux_baseChange, Algebra.TensorProduct.assoc_toLinearEquiv, LinearMap.baseChange_sub, Algebra.TensorProduct.assoc_symm_tmul, Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq, LieSubmodule.tmul_mem_baseChange_of_mem, QuadraticForm.tensorRId_toLinearEquiv, Algebra.Extension.h1Cotangentι_ext_iff, Algebra.Generators.toKaehler_tmul_D, isBaseChange, CliffordAlgebra.toBaseChange_comp_reverseOp, KaehlerDifferential.exact_kerCotangentToTensor_mapBaseChange, AlgebraTensorModule.lTensor_comp, Algebra.Extension.H1Cotangent.val_add, KaehlerDifferential.submodule_span_range_eq_ideal, LinearMap.baseChange_neg, Bialgebra.TensorProduct.coalgebra_rid_eq_algebra_rid_apply, Module.finrank_tensorProduct, Algebra.Extension.H1Cotangent.val_smul, Algebra.Presentation.differentials.comm₁₂, IsBaseChange.endHom_apply, LinearMap.mul''_apply, AlgebraTensorModule.lTensor_mul, piScalarRight_symm_single, LinearMap.baseChange_zero, LinearMap.polyCharpolyAux_map_aeval, directSumLeft_tmul, Algebra.TensorProduct.piRightHom_one, LinearMap.liftBaseChange_tmul, CommAlgCat.associator_inv_hom, IsBaseChange.toDual_apply, instIsCocomm, Algebra.TensorProduct.tensorTensorTensorComm_toLinearEquiv, Algebra.Generators.H1Cotangent.exact_map_δ', AlgebraTensorModule.map_mul, QuadraticForm.tmul_tensorLId_apply, MvPolynomial.rTensor_symm_apply_single, QuadraticForm.tensorLId_apply, KaehlerDifferential.D_tensorProductTo, Algebra.Extension.toKaehler_surjective, Rep.finsuppTensorRight_inv_hom, LieModule.toEnd_baseChange, LinearEquiv.baseChange_inv, Derivation.tensorProductTo_mul, Algebra.Generators.disjoint_ker_toKaehler_of_linearIndependent, LinearMap.BilinMap.tensorDistrib_tmul, QuadraticForm.comp_tensorRId_eq, AdicCompletion.tensor_map_id_left_eq_map, Algebra.Generators.CotangentSpace.exact, Algebra.Generators.H1Cotangent.δAux_X, counit_def, directSum_symm_lof_tmul, AdicCompletion.ofTensorProduct_tmul, MvPolynomial.rTensor_apply_monomial_tmul, Algebra.Generators.repr_CotangentSpaceMap, Module.Dual.baseChange_baseChange, LinearMap.range_liftBaseChange, AlgebraTensorModule.rTensor_mul, Algebra.Extension.H1Cotangent.map_apply_coe, CliffordAlgebra.equivBaseChange_apply, Algebra.Generators.toKaehler_cotangentSpaceBasis, Rep.finsuppTensorLeft_inv_hom, AlgebraTensorModule.map_smul_right, LinearEquiv.dilatransvection.baseChange, Module.End.baseChangeHom_apply_apply, Algebra.Generators.CotangentSpace.compEquiv_symm_inr, AlgebraTensorModule.map_comp, Module.Basis.baseChange_repr_tmul, Coalgebra.TensorProduct.assoc_tmul, AlgebraTensorModule.lift_apply, comul_tmul, Algebra.TensorProduct.basis_repr_symm_apply, AlgebraTensorModule.tensorTensorTensorComm_symm_tmul, comul_def, AlgebraTensorModule.congr_one, directSumRight'_restrict, AlgebraTensorModule.cancelBaseChange_symm_tmul, mapOfCompatibleSMul_tmul, KaehlerDifferential.derivationTensorProduct_algebraMap, AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_apply, AlgebraTensorModule.rTensor_id, Matrix.kroneckerTMulBilinear_apply, KaehlerDifferential.tensorProductTo_surjective, finsuppTensorFinsupp_symm_single, Algebra.Extension.h1Cotangentι_apply, Coalgebra.TensorProduct.assoc_symm_tmul, Algebra.Extension.cotangentComplex_injective_iff, Algebra.TensorProduct.tensorTensorTensorComm_tmul, gradedMul_algebraMap, Derivation.tensorProductTo_tmul, LinearMap.tensorEqLocus_tmul, Submodule.tensorToSpan_apply_tmul, QuadraticForm.tensorAssoc_apply, Rep.finsuppTensorLeft_hom_hom, tmul_of_gradedMul_of_tmul, Algebra.TensorProduct.equivPiOfFiniteBasis_symm_apply, AlgebraTensorModule.lTensor_one, finsuppRight_symm_apply_single, prodRight_tmul, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_symm_D_algebraMap, CliffordAlgebra.toBaseChange_involute, IsBaseChange.equiv_tmul, LinearMap.tensorProduct_apply, Algebra.Generators.snd_cotangentCompLocalizationAwayEquiv, Algebra.tensorH1CotangentOfIsLocalization_toLinearMap, Matrix.kroneckerTMulAlgEquiv_apply, Bialgebra.TensorProduct.assoc_toCoalgEquiv, ModuleCat.extendScalarsComp_hom_app_one_tmul, Coalgebra.TensorProduct.rid_symm_apply, Algebra.Generators.CotangentSpace.map_toComp_injective, finsuppLeft_apply_tmul, Module.Projective.tensorProduct, AlgebraTensorModule.map_tmul, lidOfCompatibleSMul_tmul, Coalgebra.TensorProduct.rid_toLinearEquiv, Module.Flat.iff_flat_tensorProduct, CoalgCat.rightUnitor_def, LinearMap.liftBaseChange_comp, Algebra.Extension.Hom.sub_tmul, lid'_symm_apply, AlgebraTensorModule.curry_injective, Algebra.SubmersivePresentation.sectionCotangent_comp, piScalarRight_apply, LinearEquiv.baseChange_pow, Algebra.H1Cotangent.exact_map_δ, CliffordAlgebra.ofBaseChange_tmul_one, Coalgebra.TensorProduct.rid_tmul, Algebra.Generators.H1Cotangent.δ_comp_equiv, CommAlgCat.associator_hom_hom, QuadraticMap.Isometry.tmul_apply, LinearEquiv.baseChange_symm, CliffordAlgebra.toBaseChange_ι, Module.Basis.tensorProduct_apply', AdicCompletion.ofTensorProduct_naturality, QuadraticModuleCat.toIsometry_inv_leftUnitor, Algebra.Generators.cotangentCompLocalizationAwayEquiv_symm_inl, Algebra.Generators.cotangentCompLocalizationAwayEquiv_symm_inr, Coalgebra.TensorProduct.map_toLinearMap, Submodule.baseChange_top, LieAlgebra.ExtendScalars.instLieModule, AlgebraTensorModule.lift_tmul, Algebra.SubmersivePresentation.sectionCotangent_zero_of_notMem_range, KaehlerDifferential.range_kerCotangentToTensor, Derivation.liftKaehlerDifferential_apply, Algebra.Generators.instFreeCotangentSpaceToExtension, MvPolynomial.rTensor_apply, IsBaseChange.linearMapLeftRightHom_apply, Module.Finite.base_change, AlgebraTensorModule.congr_trans, Algebra.FormallySmooth.iff_injective_cotangentComplexBaseChange, Algebra.Generators.CotangentSpace.fst_compEquiv_apply, Algebra.FormallyUnramified.comp_sec, Submodule.baseChange_span, KaehlerDifferential.tensorKaehlerEquiv_tmul_D, Coalgebra.TensorProduct.assoc_toLinearEquiv, QuadraticForm.tmul_comp_tensorAssoc, LinearMap.tensorKerEquiv_apply, LinearMap.baseChange_tmul, LinearMap.transvection.baseChange, Module.Basis.tensorProduct_repr_tmul_apply, QuadraticForm.associated_tmul, one_gradedMul, piScalarRightHom_tmul, QuadraticForm.tensorComm_symm, Algebra.TensorProduct.equivPiOfFiniteBasis_apply, Algebra.SubmersivePresentation.cotangentComplex_injective, piRight_apply, LinearEquiv.baseChange_one, AlgebraTensorModule.coe_rTensor, LieSubmodule.coe_baseChange, SpecialLinearGroup.baseChange_apply_coe, QuadraticMap.tensorDistrib_tmul, AdicCompletion.tensor_map_id_left_injective_of_injective, Algebra.kerTensorProductMapIdToAlgHomEquiv_symm_apply, LinearMap.BilinForm.baseChange_tmul, Algebra.Extension.CotangentSpace.map_comp, LinearMap.baseChange_mul, Algebra.Extension.exact_cotangentComplex_toKaehler, rank_tensorProduct', LinearMap.baseChange_id, Module.finrank_baseChange, toMatrix_comm, LieSubmodule.baseChange_top, Algebra.Generators.CotangentSpace.map_ofComp_surjective, QuadraticForm.associated_baseChange, KaehlerDifferential.map_liftBaseChange_smul, Algebra.Generators.H1Cotangent.map_comp_cotangentComplex_baseChange, LinearMap.trace_baseChange, CliffordAlgebra.ofBaseChange_comp_toBaseChange, AlgebraTensorModule.rightComm_symm, IsBaseChange.toDualBaseChange_tmul, Bialgebra.TensorProduct.assoc_symm_tmul, Algebra.Generators.CotangentSpace.fst_compEquiv, Algebra.Extension.CotangentSpace.map_comp_apply, gradedComm_gradedMul, Bialgebra.TensorProduct.assoc_toAlgEquiv, Algebra.Generators.H1Cotangent.equiv_apply, Algebra.Extension.CotangentSpace.map_comp_cotangentComplex, finsuppRight_apply_tmul_apply, LinearMap.charpoly_baseChange, finsuppRight_apply_tmul, AlgebraTensorModule.lcurry_apply, LinearMap.baseChange_add, toMatrix_map, Algebra.H1Cotangent.exact_δ_mapBaseChange, LinearMap.baseChangeHom_apply, Algebra.Generators.H1Cotangent.δ_map, LinearMap.lTensor_eqLocus_subtype_tensoreqLocusEquiv_symm, Algebra.Extension.Cotangent.map_sub_map, coe_finsuppScalarRight', AlgebraTensorModule.congr_tmul, finsuppLeft'_apply, finsuppRight_tmul_single, Algebra.Extension.cotangentComplex_mk, IsLocalizedModule.map_lTensor, Module.Basis.baseChange_linearMap, LinearEquiv.baseChange_trans, AlgebraTensorModule.tensorTensorTensorComm_tmul, derivationQuotKerSq_mk, AlgebraTensorModule.lTensor_tmul, QuadraticModuleCat.hom_hom_associator, finsuppLeft_apply_tmul_apply, instFinitePresentationTensorProduct, QuadraticModuleCat.hom_inv_associator, LieSubmodule.baseChange_bot, MvPolynomial.rTensorAlgHom_apply_eq
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mk 📖 | CompOp | — |
tmul 📖 | CompOp | 638 mathmath: KaehlerDifferential.kerCotangentToTensor_toCotangent, Algebra.FormallyUnramified.one_tmul_mul_elem, Submodule.rTensorOne_symm_apply, Algebra.Generators.baseChange_val, ModuleCat.MonoidalCategory.braiding_hom_apply, inner_tmul, LieModule.liftLie_apply, Coalgebra.lTensor_counit_comul, ext_iff_inner_left, Algebra.TensorProduct.intCast_def', Module.Basis.tensorProduct_apply, AlgebraTensorModule.rid_symm_apply, Algebra.TensorProduct.prodRight_tmul_fst, IsGroupLikeElem.comul_eq_tmul_self, MvPolynomial.rTensor_apply_tmul_apply, PiTensorProduct.tmulEquiv_symm_apply, Submodule.mulMap_tmul, MvPolynomial.scalarRTensor_apply_monomial_tmul, LaurentPolynomial.comul_T, finsuppTensorFinsupp_apply, equivFinsuppOfBasisLeft_symm_apply, Submodule.tensorEquivSpan_apply_tmul, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul', Algebra.Generators.cotangentSpaceBasis_apply, kroneckerTMulAlgEquiv_symm_single_tmul, ModuleCat.extendScalarsId_hom_app_one_tmul, Algebra.IsPushout.equiv_symm_algebraMap_left, Representation.Coinvariants.mk_inv_tmul, Polynomial.fiberEquivQuotient_tmul, LinearMap.tensorKer_tmul, Module.Invertible.tmul_comm, star_tmul, piScalarRight_symm_algebraMap, Algebra.TensorProduct.natCast_def', AlgebraTensorModule.rid_tmul, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul, Coalgebra.sum_map_tmul_counit_eq, Algebra.IsPushout.cancelBaseChange_tmul, span_tmul_eq_top, tensorTensorTensorComm_tmul, gradedComm_tmul_one, AlgebraTensorModule.congr_symm_tmul, Coalgebra.sum_tmul_counit_eq, Representation.ofCoinvariantsTprodLeftRegular_mk_tmul_single, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left, ModuleCat.monoidalClosed_uncurry, MonoidAlgebra.tensorEquiv.invFun_tmul, KaehlerDifferential.cotangentComplexBaseChange_tmul, SemimoduleCat.MonoidalCategory.rightUnitor_hom_apply, Matrix.kroneckerTMul_zero, smul_tmul, Algebra.TensorProduct.prodRight_symm_tmul, IsLocalization.mk'_tmul, InnerProductSpace.canonicalCovariantTensor_eq_sum, MvPolynomial.scalarRTensor_apply_X_tmul_apply, ext_iff_inner_right_threefold', Algebra.FormallyUnramified.finite_of_free_aux, Matrix.kroneckerTMul_assoc', Algebra.TensorProduct.algebraMap_apply, AlgebraTensorModule.rightComm_symm_tmul, Algebra.PreSubmersivePresentation.baseChange_jacobian, Algebra.IsPushout.cancelBaseChange_symm_tmul, Submodule.val_mulMap'_tmul, directSum_lof_tmul_lof, KaehlerDifferential.kerToTensor_apply, RingHom.SurjectiveOnStalks.exists_mul_eq_tmul, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right, quotientTensorQuotientEquiv_symm_apply_mk_tmul, zero_prodMap_dualTensorHom, Algebra.TensorProduct.basis_apply, LinearMap.liftBaseChange_one_tmul, ModuleCat.extendRestrictScalarsAdj_homEquiv_apply, Algebra.TensorProduct.piScalarRight_tmul, liftAux_tmul, Module.endTensorEndAlgHom_apply, tensorIteratedFDerivTwo_eq_iteratedFDeriv, finsuppTensorFinsupp'_symm_single_eq_tmul_single_one, Rep.finsuppToCoinvariantsTensorFree_single, PolyEquivTensor.toFunAlgHom_apply_tmul, Coalgebra.sum_counit_tmul_eq, Representation.Coinvariants.mk_tmul_inv, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_single, Algebra.TensorProduct.assoc_tmul, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, directLimitRight_tmul_of, Algebra.TensorProduct.map_tmul, LinearMap.rTensor_tmul, equivFinsuppOfBasisLeft_apply_tmul_apply, leftComm_tmul, Algebra.TensorProduct.algEquivIncludeRange_symm_tmul, Algebra.Generators.cotangentSpaceBasis_repr_one_tmul, Algebra.TensorProduct.leftComm_tmul, SemimoduleCat.MonoidalCategory.tensorHom_tmul, Algebra.TensorProduct.includeRight_apply, ModuleCat.MonoidalCategory.associator_hom_apply, Finsupp.linearCombination_one_tmul, Algebra.TensorProduct.basis_repr_tmul, ModuleCat.MonoidalCategory.tensorHom_tmul, KaehlerDifferential.mapBaseChange_tmul, tmul_sub, Algebra.Generators.H1Cotangent.δAux_C, gradedComm_algebraMap_tmul, liftAddHom_tmul, Coalgebra.sum_map_tmul_tmul_eq, equivFinsuppOfBasisRight_apply_tmul, Algebra.Extension.CotangentSpace.map_tmul, LocalizedModule.equivTensorProduct_symm_apply_tmul_one, SemimoduleCat.MonoidalCategory.whiskerRight_apply, LocalizedModule.equivTensorProduct_apply_mk, Algebra.TensorProduct.lid_tmul, equivFinsuppOfBasisLeft_apply_tmul, Algebra.TensorProduct.tensorTensorTensorComm_symm_tmul, isGroupLikeElem_iff, LinearMap.tensorKerEquivOfSurjective_symm_tmul, Algebra.smul_def, tensorIteratedFDerivWithinTwo_eq_iteratedFDerivWithin, PointedCone.tmul_mem_maxTensorProduct, Algebra.TensorProduct.includeLeft_apply, LocalizedModule.equivTensorProduct_symm_apply_tmul, finsuppScalarRight_apply_tmul, Algebra.TensorProduct.right_algebraMap_apply, Coalgebra.TensorProduct.lid_tmul, mk_apply, SemimoduleCat.MonoidalCategory.rightUnitor_inv_apply, LieAlgebra.LoopAlgebra.toFinsupp_symm_single, Subalgebra.LinearDisjoint.mulMapLeftOfSupEqTop_symm_apply, finsuppTensorFinsupp'_single_tmul_single, dualTensorHom_apply, LinearEquiv.lTensor_tmul, quotientTensorEquiv_symm_apply_mk_tmul, MonoidAlgebra.scalarTensorEquiv_tmul, FGModuleCat.FGModuleCatEvaluation_apply, neg_tmul, PresheafOfModules.Monoidal.tensorObj_map_tmul, LieAlgebra.coe_rootSpaceWeightSpaceProduct_tmul, finsuppTensorFinsuppLid_symm_single_smul, tmul_smul, SemiconjBy.tmul, MvPolynomial.scalarRTensor_apply_tmul, prodLeft_tmul, MultilinearMap.domCoprodDep_apply, ModuleCat.monoidalClosed_curry, AddMonoidAlgebra.tensorEquiv.invFun_tmul, finsuppTensorFinsupp'_symm_single_mul, MatrixEquivTensor.invFun_algebraMap, Algebra.TensorProduct.productMap_left_apply, Subalgebra.lTensorBot_one_tmul, PolyEquivTensor.toFunLinear_mul_tmul_mul, ModuleCat.MonoidalCategory.leftUnitor_hom_apply, KaehlerDifferential.tensorKaehlerEquivBase_tmul, finsuppLeft_symm_apply_single, Algebra.TensorProduct.productMap_apply_tmul, LinearMap.BilinForm.tensorDistrib_tmul, AlgebraTensorModule.mk_apply, QuadraticForm.baseChange_tmul, IsTensorProduct.equiv_symm_apply, ext_iff_inner_left_threefold', finsuppTensorFinsupp'_apply_apply, LinearMap.mul'_apply, AlgebraTensorModule.rTensor_tmul, prodLeft_symm_tmul, ext_iff_inner_left_threefold, Algebra.TensorProduct.lmul'_apply_tmul, tmul_eq_smul_one_tmul, Algebra.Generators.H1Cotangent.δAux_monomial, map₂_apply_tmul, dualDistribEquivOfBasis_symm_apply, SemimoduleCat.MonoidalCategory.tensorLift_tmul, OrthonormalBasis.tensorProduct_repr_tmul_apply', Algebra.Generators.cotangentSpaceBasis_repr_tmul, LinearMap.liftBaseChangeEquiv_symm_apply, Matrix.smul_kroneckerTMul, Algebra.Extension.Hom.sub_one_tmul, nnnorm_tmul, lift.tmul', assoc_tmul, MvPolynomial.rTensor_apply_X_tmul, LinearIndepOn.tmul_of_flat_right, Bialgebra.TensorProduct.assoc_tmul, KaehlerDifferential.tensorKaehlerEquiv_tmul, Algebra.Generators.H1Cotangent.δAux_toAlgHom, KaehlerDifferential.D_apply, InnerProductSpace.AlgebraOfCoalgebra.mul_def, AlgebraTensorModule.leftComm_tmul, tmul_zero, gradedComm_tmul_of_zero, equivFinsuppOfBasisRight_apply_tmul_apply, polyEquivTensor_symm_apply_tmul, KaehlerDifferential.one_smul_sub_smul_one_mem_ideal, congr_tmul, MvPolynomial.tensorEquivSum_one_tmul_C, MvPolynomial.rTensor_apply_tmul, AlgHom.mulLeftRight_apply, Algebra.TensorProduct.commRight_tmul, transpose_dualTensorHom, AlgebraTensorModule.assoc_tmul, Submodule.coe_tensorSpanEquivSpan_apply_tmul, directSumLeft_tmul_lof, AlgebraTensorModule.leftComm_symm_tmul, AlgebraTensorModule.rightComm_tmul, AlgebraTensorModule.assoc_symm_tmul, algebraMap_gradedMul, MonoidAlgebra.tensorEquiv_symm_single, ModuleCat.MonoidalCategory.rightUnitor_hom_apply, lid_symm_apply, tensorQuotEquivQuotSMul_tmul_mk, finsuppTensorFinsupp_single, counit_tmul, CompatibleSMul.smul_tmul, lid_tmul, FGModuleCat.FGModuleCatCoevaluation_apply_one, LinearMap.BilinMap.baseChange_tmul, piRight_symm_apply, AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_symm_of, lift.tmul, finsuppTensorFinsupp'_symm_single_eq_single_one_tmul, lTensorHomToHomLTensor_apply, Matrix.single_kroneckerTMul_single, Algebra.TensorProduct.tmul_mul_tmul, Coalgebra.sum_counit_tmul_map_eq, AlgebraTensorModule.cancelBaseChange_tmul, LinearMap.mulRight_tmul, ModuleCat.MonoidalCategory.tensorLift_tmul, LieModule.map_tmul, finsuppScalarRight_apply_tmul_apply, SemimoduleCat.MonoidalCategory.tensorμ_apply, LinearEquiv.baseChange_tmul, Ideal.ResidueField.exists_smul_eq_tmul_one, kroneckerLinearEquiv_symm_kronecker, finsuppTensorFinsuppRid_symm_single_smul, prodRight_symm_tmul, ext_iff_inner_right, exists_finsupp_left, AlgebraTensorModule.dualDistrib_apply, piRight_symm_single, Submodule.lTensorOne'_tmul, Submodule.rTensorOne'_tmul_one, baseChange_ext_iff, Submodule.rTensorOne'_tmul, Matrix.conjTranspose_kroneckerTMul, Algebra.TensorProduct.basisAux_tmul, MvPolynomial.algebraTensorAlgEquiv_symm_X, AlternatingMap.domCoprod'_apply, tensorKaehlerQuotKerSqEquiv_symm_tmul_D, toMatrix_dualTensorHom, LinearIndependent.tmul_of_flat_left, Algebra.Generators.H1Cotangent.δAux_ofComp, Matrix.diagonal_kroneckerTMul_diagonal, AlgebraTensorModule.homTensorHomMap_apply, RCLike.inner_tmul_eq, Coalgebra.TensorProduct.map_tmul, Matrix.diagonal_kroneckerTMul, lid'_apply_tmul, enorm_tmul, Module.Basis.baseChange_apply, Algebra.TensorProduct.basis_repr_symm_apply', groupHomology.H1AddEquivOfIsTrivial_single, kroneckerTMulLinearEquiv_symm_kroneckerTMul, PointedCone.tmul_subset_maxTensorProduct, CliffordAlgebra.ofBaseChange_tmul_ι, Algebra.TensorProduct.rid_tmul, Submodule.rTensorOne_tmul, zero_tmul, IsBaseChange.equiv_symm_apply, congr_symm_tmul, Algebra.TensorProduct.cancelBaseChange_tmul, Algebra.TensorProduct.mul_one, sum_tmul, finsuppScalarRight_symm_apply_single, tmul_sum, sectionOfRetractionKerToTensorAux_prop, CliffordAlgebra.ofBaseChangeAux_ι, PolynomialLaw.one_tmul_ground, LinearEquiv.rTensor_symm_tmul, SemimoduleCat.MonoidalCategory.braiding_hom_apply, piRightHom_tmul, quotientTensorQuotientEquiv_apply_tmul_mk_tmul_mk, tensorKaehlerQuotKerSqEquiv_tmul_D, tensorQuotientEquiv_apply_mk_tmul, SemimoduleCat.MonoidalCategory.braiding_inv_apply, Algebra.FormallyUnramified.one_tmul_sub_tmul_one_mul_elem, QuadraticForm.tensorDistrib_tmul, LieModule.toModuleHom_apply, directSumRight_tmul_lof, OrthonormalBasis.tensorProduct_apply', MultilinearMap.domCoprod'_apply, MvPolynomial.universalFactorizationMapPresentation_relation, ModuleCat.ExtendScalars.smul_tmul, Module.Flat.linearIndependent_one_tmul, exists_multiset, kroneckerTMulLinearEquiv_tmul, Subalgebra.rTensorBot_tmul_one, Module.Dual.baseChange_apply_tmul, Algebra.IsPushout.cancelBaseChangeAux_symm_tmul, Commute.tmul, directSumLeft_symm_lof_tmul, Matrix.kroneckerTMul_add, PointedCone.tmul_subset_minTensorProduct, sum_tmul_eq_zero_of_vanishesTrivially, tensorQuotEquivQuotSMul_symm_mk, Module.Relations.Solution.tensor_var, MonoidAlgebra.tensorEquiv_tmul, ite_tmul, Algebra.Presentation.tensorModelOfHasCoeffsEquiv_tmul, LieAlgebra.ExtendScalars.bracket_tmul, rid_tmul, Submodule.tmul_mem_baseChange_of_mem, matrixEquivTensor_apply_single, CharacterModule.homEquiv_symm_apply_apply_apply, Algebra.TensorProduct.cancelBaseChange_symm_tmul, MvPolynomial.universalFactorizationMapPresentation_algebra_algebraMap, ModuleCat.ExtendScalars.map_tmul, MvPolynomial.coeff_rTensorAlgHom_tmul, PiTensorProduct.tmulEquivDep_symm_apply, Submodule.rTensorOne_tmul_one, ModuleCat.free_μ_freeMk_tmul_freeMk, MatrixEquivTensor.invFun_smul, Rep.diagonalSuccIsoTensorTrivial_hom_hom_single, single_tmul, finsuppTensorFinsuppRid_single_tmul_single, LieAlgebra.LoopAlgebra.toFinsupp_single_tmul, Algebra.Presentation.tensorModelOfHasCoeffsHom_tmul, Algebra.Extension.contangentEquiv_tmul, finsuppScalarLeft_apply_tmul_apply, Algebra.TensorProduct.assoc_symm_tmul, matrixEquivTensor_apply_symm, ModuleCat.FreeMonoidal.μIso_hom_freeMk_tmul_freeMk, LieSubmodule.tmul_mem_baseChange_of_mem, Bialgebra.TensorProduct.map_tmul, ModuleCat.MonoidalCategory.rightUnitor_inv_apply, PiTensorProduct.tmulEquivDep_apply, Algebra.TensorProduct.linearEquivIncludeRange_symm_tmul, Algebra.TensorProduct.algEquivIncludeRange_tmul, LieModule.lift_apply, Algebra.Generators.toKaehler_tmul_D, LieModule.lie_tmul_right, GradedTensorProduct.auxEquiv_tmul, Subalgebra.lTensorBot_symm_apply, groupHomology.H1ToTensorOfIsTrivial_H1π_single, KaehlerDifferential.submodule_span_range_eq_ideal, SMul.aux_of, sectionOfRetractionKerToTensor_algebraMap, gradedComm_of_zero_tmul, ModuleCat.MonoidalCategory.leftUnitor_inv_apply, Algebra.TensorProduct.tmul_pow, ModuleCat.MonoidalCategory.tensorμ_apply, piScalarRight_symm_single, MvPolynomial.ker_eval₂Hom_universalFactorizationMap, PolyEquivTensor.toFunAlgHom_apply_tmul_eq_smul, sub_tmul, Algebra.TensorProduct.one_mul, TensorPower.gMul_def, Subalgebra.tmul_mem_baseChange, SemimoduleCat.MonoidalCategory.associator_inv_apply, directSumLeft_tmul, LinearMap.liftBaseChange_tmul, quotTensorEquivQuotSMul_symm_mk, Algebra.IsPushout.equiv_tmul, AddMonoidAlgebra.tensorEquiv_tmul, PolyEquivTensor.toFunLinear_tmul_apply, smul_tmul', SemimoduleCat.MonoidalCategory.whiskerLeft_apply, Module.FaithfullyFlat.one_tmul_eq_zero_iff, eq_repr_basis_left, MvPolynomial.rTensor_symm_apply_single, LinearMap.BilinForm.tensorDistribEquiv_tmul, leftComm_symm_tmul, AddMonoidAlgebra.tensorEquiv_symm_single, LieModule.toEnd_baseChange, contractLeft_apply, LinearMap.BilinMap.tensorDistrib_tmul, LineDeriv.tensorLineDerivTwo_eq_lineDerivOp_lineDerivOp, range_map_eq_span_tmul, Algebra.TensorProduct.comm_symm_tmul, Coalgebra.sum_tmul_tmul_eq, MonoidAlgebra.scalarTensorEquiv_symm_single, Algebra.TensorProduct.tmul_one_eq_one_tmul, LinearMap.mulLeft_tmul, Matrix.add_kroneckerTMul, Algebra.TensorProduct.quotIdealMapEquivTensorQuot_symm_tmul, directSum_symm_lof_tmul, LinearIndepOn.tmul_of_flat_left, tmul_single, MultilinearMap.domCoprod_apply, PolyEquivTensor.invFun_monomial, Representation.smul_tprod_one_asModule, AdicCompletion.ofTensorProduct_tmul, MvPolynomial.rTensor_apply_monomial_tmul, LinearIndependent.tmul_of_isDomain, PiTensorProduct.tmulEquiv_apply, dualDistribInvOfBasis_apply, dualTensorHom_prodMap_zero, PolyEquivTensor.toFunLinear_one_tmul_one, IsLocalization.tmul_mk', quotientTensorEquiv_apply_tmul_mk, Algebra.TensorProduct.piRight_tmul, rightComm_tmul, exists_finsupp_right, Representation.coinvariantsTprodLeftRegularLEquiv_symm_apply, finsuppScalarLeft_apply_tmul, directSumRight_tmul, gradedComm_tmul_algebraMap, dist_tmul_le, Subalgebra.lTensorBot_tmul, MvPolynomial.tensorEquivSum_X_tmul_X, ModuleCat.MonoidalCategory.whiskerRight_apply, ModuleCat.free_δ_freeMk, MvPolynomial.coeff_rTensorAlgHom_monomial_tmul, MvPolynomial.algebraTensorAlgEquiv_symm_map, rid_symm_apply, Algebra.TensorProduct.productMap_right_apply, MvPolynomial.tensorEquivSum_C_tmul_one, Algebra.Extension.tensorCotangentInvFun_smul_mk, Module.Basis.baseChange_repr_tmul, Coalgebra.TensorProduct.assoc_tmul, comul_tmul, Algebra.TensorProduct.basis_repr_symm_apply, finsuppTensorFinsuppLid_apply_apply, polyEquivTensor_apply, AlgebraTensorModule.tensorTensorTensorComm_symm_tmul, Algebra.Presentation.algebraTensorAlgEquiv_symm_relation, lcurry_apply, curry_apply, Subalgebra.LinearDisjoint.val_mulMap_tmul, map_tmul, Matrix.kroneckerTMul_smul, smul_tmul_smul, Module.Invertible.rTensorEquiv_symm_apply_apply, Algebra.TensorProduct.algebraMap_apply', Algebra.TensorProduct.Algebra.TensorProduct.commRight_symm_tmul, Algebra.TensorProduct.lift_tmul, AlgebraTensorModule.cancelBaseChange_symm_tmul, lift.equiv_symm_apply, Subalgebra.rTensorBot_symm_apply, Subalgebra.LinearDisjoint.mulMapLeftOfSupEqTop_tmul, ModuleCat.FreeMonoidal.μIso_inv_freeMk, mapOfCompatibleSMul_tmul, KaehlerDifferential.derivationTensorProduct_algebraMap, Matrix.kroneckerTMulBilinear_apply, Coalgebra.rTensor_counit_comul, finsuppTensorFinsupp_symm_single, comp_dualTensorHom, Coalgebra.TensorProduct.assoc_symm_tmul, Algebra.TensorProduct.natCast_def, Algebra.TensorProduct.tensorTensorTensorComm_tmul, gradedMul_algebraMap, Algebra.Presentation.tensorModelOfHasCoeffsEquiv_symm_tmul, Matrix.trace_kroneckerTMul, IsIntegral.tmul, Derivation.tensorProductTo_tmul, homTensorHomMap_apply, Submodule.lTensorOne_symm_apply, LinearMap.tensorEqLocus_tmul, tmul_add, AddMonoidAlgebra.scalarTensorEquiv_symm_single, sectionOfRetractionKerToTensorAux_algebraMap, Submodule.tensorToSpan_apply_tmul, Algebra.baseChange_lmul, SemimoduleCat.MonoidalCategory.leftUnitor_inv_apply, finsuppTensorFinsuppRid_apply_apply, tmul_of_gradedMul_of_tmul, Matrix.mul_kroneckerTMul_mul, Submodule.lTensorOne'_one_tmul, map_dualTensorHom, finsuppRight_symm_apply_single, gradedComm_one_tmul, prodRight_tmul, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_symm_D_algebraMap, Algebra.TensorProduct.quotIdealMapEquivTensorQuot_mk, IsBaseChange.equiv_tmul, IsAddUnit.tmul_left, Rep.coinvariantsTensorMk_apply, finsuppTensorFinsuppLid_single_tmul_single, Matrix.kroneckerTMul_diagonal, MvPolynomial.algebraTensorAlgEquiv_tmul, Algebra.tmul_comm, Algebra.TensorProduct.comm_tmul, ModuleCat.extendScalarsComp_hom_app_one_tmul, contractRight_apply, KaehlerDifferential.span_range_eq_ideal, Coalgebra.TensorProduct.rid_symm_apply, Algebra.TensorProduct.intCast_def, add_tmul, tensorTensorTensorAssoc_symm_tmul, finsuppLeft_apply_tmul, Algebra.TensorProduct.opAlgEquiv_tmul, AlgebraTensorModule.map_tmul, lidOfCompatibleSMul_tmul, Bialgebra.TensorProduct.rid_symm_apply, Submodule.lTensorOne_tmul, norm_tmul, directLimitLeft_tmul_of, MvPolynomial.aeval_one_tmul, Submodule.LinearDisjoint.val_mulMap_tmul, Algebra.Extension.Hom.sub_tmul, lid'_symm_apply, IsAlgebraic.tmul, tmul_ite, MvPolynomial.universalFactorizationMapPresentation_algebra_smul, MvPolynomial.tensorEquivSum_one_tmul_X, FGModuleCat.FGModuleCatEvaluation_apply', Matrix.det_kroneckerTMul, exists_finset, LinearEquiv.lTensor_symm_tmul, CliffordAlgebra.ofBaseChange_tmul_one, Coalgebra.TensorProduct.rid_tmul, MvPolynomial.universalFactorizationMapPresentation_val, gradedCommAux_lof_tmul, Algebra.TensorProduct.prodRight_tmul, Algebra.TensorProduct.prodRight_tmul_snd, directLimitLeft_symm_of_tmul, Algebra.IsPushout.equiv_symm_algebraMap_right, Bialgebra.TensorProduct.rid_tmul, CliffordAlgebra.toBaseChange_ι, PointedCone.tmul_mem_minTensorProduct, Bialgebra.TensorProduct.lid_tmul, comm_tmul, dualDistrib_apply, Module.Basis.tensorProduct_apply', MvPolynomial.scalarRTensor_symm_apply_single, Representation.smul_one_tprod_asModule, Subalgebra.val_mulMap'_tmul, Rep.leftRegularTensorTrivialIsoFree_hom_hom_single_tmul_single, Matrix.kroneckerTMul_apply, AlgebraTensorModule.lift_tmul, Matrix.kroneckerTMul_assoc, ModuleCat.extendRestrictScalarsAdj_unit_app_apply, LinearIndependent.tmul_of_flat_right, KaehlerDifferential.DLinearMap_apply, ModuleCat.MonoidalCategory.whiskerLeft_apply, vanishesTrivially_iff_sum_tmul_eq_zero, Algebra.moduleAux_apply, map_range_eq_span_tmul, Coalgebra.Repr.eq, nndist_tmul_le, Submodule.lTensorOne_one_tmul, Matrix.one_kroneckerTMul_one, KaehlerDifferential.tensorKaehlerEquiv_tmul_D, Bialgebra.TensorProduct.lid_symm_apply, AddMonoidAlgebra.scalarTensorEquiv_tmul, PointedCone.mem_maxTensorProduct, rTensorHomToHomRTensor_apply, fromDirectLimit_of_tmul, LinearMap.baseChange_tmul, LinearMap.transvection.baseChange, Module.Basis.tensorProduct_repr_tmul_apply, MvPolynomial.algebraTensorAlgEquiv_symm_monomial, PolynomialLaw.ground_apply, OrthonormalBasis.tensorProduct_apply, finsuppScalarLeft_symm_apply_single, piScalarRightHom_tmul, Algebra.TensorProduct.adjoin_tmul_eq_top, Subalgebra.mulMap_tmul, Algebra.TensorProduct.piScalarRight_tmul_apply, ModuleCat.extendScalarsId_inv_app_apply, Algebra.TensorProduct.lidOfCompatibleSMul_tmul, ModuleCat.MonoidalCategory.braiding_inv_apply, MvPolynomial.tensorEquivSum_X_tmul_one, QuadraticMap.tensorDistrib_tmul, tensorQuotientEquiv_symm_apply_tmul_mk, Algebra.kerTensorProductMapIdToAlgHomEquiv_symm_apply, matrixEquivTensor_apply, MatrixEquivTensor.toFunAlgHom_apply, LinearMap.BilinForm.baseChange_tmul, gradedComm_of_tmul_of, Algebra.TensorProduct.opAlgEquiv_symm_tmul, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, MvPolynomial.scalarRTensor_apply_tmul_apply, SemimoduleCat.MonoidalCategory.leftUnitor_hom_apply, directLimitRight_symm_of_tmul, Algebra.isEpi_iff_forall_one_tmul_eq, Algebra.TensorProduct.lid_symm_apply, Orthonormal.tmul, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, assoc_symm_tmul, tmul_neg, Algebra.TensorProduct.leftComm_symm_tmul, comm_symm_tmul, MvPolynomial.tensorEquivSum_C_tmul_C, Subalgebra.rTensorBot_tmul, equivFinsuppOfBasisRight_symm_apply, exists_sum_tmul_eq, LaurentPolynomial.comul_C_mul_T_self, MultilinearMap.domCoprodDep'_apply, Algebra.FormallyUnramified.iff_exists_tensorProduct, IsBaseChange.toDualBaseChange_tmul, Bialgebra.TensorProduct.assoc_symm_tmul, PolynomialLaw.one_tmul_ground_apply', ModuleCat.ExtendScalars.hom_ext_iff, Algebra.TensorProduct.rid_symm_apply, LinearEquiv.rTensor_tmul, Coalgebra.TensorProduct.lid_symm_apply, finsuppRight_apply_tmul_apply, directSumRight_symm_lof_tmul, LieAlgebra.ExtendScalars.map_apply_tmul, Algebra.TensorProduct.mapOfCompatibleSMul_tmul, LieAlgebra.rootSpaceProduct_tmul, Ideal.Fiber.exists_smul_eq_one_tmul, finsuppRight_apply_tmul, LinearIndepOn.tmul_of_isDomain, polyEquivTensor_symm_apply_tmul_eq_smul, vanishesTrivially_iff_sum_tmul_eq_zero_of_rTensor_injective, Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single, ext_iff_inner_right_threefold, OrthonormalBasis.tensorProduct_repr_tmul_apply, CommSemiring.comul_apply, LinearMap.lTensor_tmul, KaehlerDifferential.mulActionBaseChange_smul_tmul, Algebra.TensorProduct.mul_apply, lidIsometry_symm_apply, Algebra.TensorProduct.linearEquivIncludeRange_tmul, AlgebraTensorModule.congr_tmul, Algebra.TensorProduct.adjoin_one_tmul_image_eq_top, lift.equiv_apply, finsuppRight_tmul_single, Algebra.Extension.cotangentComplex_mk, retractionOfSectionOfKerSqZero_tmul_D, Algebra.TensorProduct.one_def, toDirectLimit_tmul_of, Algebra.TensorProduct.includeLeftRingHom_apply, AlgebraTensorModule.tensorTensorTensorComm_tmul, quotTensorEquivQuotSMul_mk_tmul, ModuleCat.MonoidalCategory.associator_inv_apply, derivationQuotKerSq_mk, uncurry_apply, Rep.leftRegularTensorTrivialIsoFree_inv_hom_single_single, edist_tmul_le, AlgebraTensorModule.lTensor_tmul, IsAddUnit.tmul_right, includeRight_lid, Matrix.zero_kroneckerTMul, tensorTensorTensorAssoc_tmul, SemimoduleCat.MonoidalCategory.associator_hom_apply, finsuppLeft_apply_tmul_apply, Module.Presentation.tensor_var, eq_repr_basis_right, Algebra.Presentation.tensorModelOfHasCoeffsInv_aeval_val, kroneckerLinearEquiv_tmul
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uniqueLeft 📖 | CompOp | — |
uniqueRight 📖 | CompOp | — |
zero 📖 | CompOp | 79 mathmath: finsuppRight_apply, Module.Flat.iff_lTensor_exact', Module.FaithfullyFlat.iff_exact_iff_lTensor_exact, MvPolynomial.rTensor_apply_tmul_apply, finsuppTensorFinsupp_apply, kroneckerTMulAlgEquiv_symm_single_tmul, Matrix.kroneckerTMul_zero, Module.Flat.lTensor_exact, Module.FaithfullyFlat.lTensor_exact_iff_exact, zero_smul, Algebra.instIsReducedTensorProductOfIsAlgebraicOfIsGeometricallyReduced, Algebra.isGeometricallyReduced_iff, finsuppLeft_smul', smul_zero, finsuppLeft_symm_apply_single, Algebra.IsGeometricallyReduced.isReduced_algebraicClosure_tensorProduct, Module.FaithfullyFlat.rTensor_exact_iff_exact, PrimeSpectrum.mem_image_comap_basicOpen, MvPolynomial.rTensor_apply_X_tmul, lTensor_exact, tmul_zero, Module.Flat.iff_lTensor_exact, Module.Flat.rTensor_exact, MvPolynomial.rTensor_apply_tmul, Module.FaithfullyFlat.iff_exact_iff_rTensor_exact, kroneckerTMulLinearEquiv_one, PolynomialLaw.toFun_zero, finsuppTensorFinsupp_single, PolynomialLaw.zero_def, Matrix.single_kroneckerTMul_single, finsuppLeft_apply, piRight_symm_single, MvPolynomial.rTensorAlgHom_toLinearMap, Rep.finsuppTensorRight_hom_hom, Matrix.diagonal_kroneckerTMul_diagonal, Matrix.diagonal_kroneckerTMul, zero_tmul, Algebra.FormallyUnramified.one_tmul_sub_tmul_one_mul_elem, Module.Flat.iff_rTensor_exact', sum_tmul_eq_zero_of_vanishesTrivially, ite_tmul, single_tmul, Module.Flat.iff_rTensor_exact, rTensor_exact, Module.FaithfullyFlat.one_tmul_eq_zero_iff, MvPolynomial.rTensor_symm_apply_single, Rep.finsuppTensorRight_inv_hom, tmul_single, MvPolynomial.rTensor_apply_monomial_tmul, isNilpotent_tensor_residueField_iff, Rep.finsuppTensorLeft_inv_hom, MvPolynomial.coeff_rTensorAlgHom_monomial_tmul, AlternatingMap.domCoprod.summand_eq_zero_of_smul_invariant, finsuppTensorFinsupp_symm_single, LinearMap.rTensor_exact_iff_lTensor_exact, Rep.finsuppTensorLeft_hom_hom, finsuppRight_symm_apply_single, Matrix.kroneckerTMul_diagonal, finsuppLeft_apply_tmul, MatrixEquivTensor.invFun_zero, tmul_ite, Algebra.H1Cotangent.exact_map_δ, Algebra.Generators.cotangentCompLocalizationAwayEquiv_symm_inr, MvPolynomial.rTensor_apply, vanishesTrivially_iff_sum_tmul_eq_zero, PrimeSpectrum.mem_image_comap_zeroLocus_sdiff, Matrix.one_kroneckerTMul_one, neg_add_cancel, KaehlerDifferential.mulActionBaseChange_smul_zero, Algebra.FormallyUnramified.iff_exists_tensorProduct, finsuppRight_apply_tmul_apply, finsuppRight_apply_tmul, vanishesTrivially_iff_sum_tmul_eq_zero_of_rTensor_injective, finsuppLeft'_apply, finsuppRight_tmul_single, Matrix.zero_kroneckerTMul, finsuppLeft_apply_tmul_apply, AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero, MvPolynomial.rTensorAlgHom_apply_eq
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«term_⊗[_]_» 📖 | CompOp | — |
«term_⊗_» 📖 | CompOp | — |
«term_⊗ₜ[_]_» 📖 | CompOp | — |
«term_⊗ₜ_» 📖 | CompOp | — |