Documentation Verification Report

IsIso

📁 Source: Mathlib/AlgebraicGeometry/Morphisms/IsIso.lean

Statistics

MetricCount
DefinitionsIsIso
1
TheoremsinstHasAffinePropertyIsomorphismsSchemeAndIsAffineIsIsoCommRingCatAppTop, instIsZariskiLocalAtTargetMonomorphismsScheme, isIso_SpecMap_iff, isIso_iff_isOpenImmersion_and_surjective, isomorphisms_eq_isOpenImmersion_inf_surjective, isomorphisms_eq_stalkwise
6
Total7

AlgebraicGeometry

Theorems

NameKindAssumesProvesValidatesDepends On
instHasAffinePropertyIsomorphismsSchemeAndIsAffineIsIsoCommRingCatAppTop 📖mathematicalHasAffineProperty
CategoryTheory.MorphismProperty.isomorphisms
Scheme
Scheme.instCategory
IsAffine
CategoryTheory.IsIso
CommRingCat
CommRingCat.instCategory
CategoryTheory.Functor.obj
Opposite
TopologicalSpace.Opens
TopCat.carrier
PresheafedSpace.carrier
SheafedSpace.toPresheafedSpace
LocallyRingedSpace.toSheafedSpace
Scheme.toLocallyRingedSpace
TopCat.str
CategoryTheory.Category.opposite
Preorder.smallCategory
PartialOrder.toPreorder
TopologicalSpace.Opens.instPartialOrder
PresheafedSpace.presheaf
Opposite.op
Scheme.Opens
Top.top
OrderTop.toTop
Preorder.toLE
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
TopologicalSpace.Opens.instCompleteLattice
SheafedSpace.instTopologicalSpaceCarrierCarrier
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
Scheme.Hom.appTop
CategoryTheory.MorphismProperty.arrow_mk_iso_iff
CategoryTheory.MorphismProperty.RespectsIso.isomorphisms
instIsIsoSchemeMapOfCommRingCat
IsAffine.of_isIso
Scheme.Hom.instIsIsoCommRingCatApp
HasAffineProperty.of_isZariskiLocalAtTarget
Scheme.instIsLocalAtTargetIsomorphismsZariskiPrecoverage
instIsZariskiLocalAtTargetMonomorphismsScheme 📖mathematicalIsZariskiLocalAtTarget
CategoryTheory.MorphismProperty.monomorphisms
Scheme
Scheme.instCategory
Scheme.Pullback.instHasPullbacks
instIsZariskiLocalAtTargetDiagonalScheme
Scheme.instIsLocalAtTargetIsomorphismsZariskiPrecoverage
CategoryTheory.MorphismProperty.diagonal_isomorphisms
isIso_SpecMap_iff 📖mathematicalCategoryTheory.IsIso
Scheme
Scheme.instCategory
Spec
Spec.map
Function.Bijective
CommRingCat.carrier
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
CommRingCat.commRing
RingHom.instFunLike
CommRingCat.Hom.hom
CategoryTheory.ConcreteCategory.isIso_iff_bijective
CommRingCat.forgetReflectIsos
CategoryTheory.MorphismProperty.isomorphisms.iff
CategoryTheory.MorphismProperty.arrow_mk_iso_iff
CategoryTheory.MorphismProperty.RespectsIso.isomorphisms
Scheme.Hom.instIsIsoCommRingCatApp
instIsIsoSchemeMapOfCommRingCat
isIso_iff_isOpenImmersion_and_surjective 📖mathematicalCategoryTheory.IsIso
Scheme
Scheme.instCategory
IsOpenImmersion
Surjective
surjective_iff
TopCat.epi_iff_surjective
isIso_iff_isOpenImmersion_and_epi_base
isomorphisms_eq_isOpenImmersion_inf_surjective 📖mathematicalCategoryTheory.MorphismProperty.isomorphisms
Scheme
Scheme.instCategory
CategoryTheory.MorphismProperty
CategoryTheory.Category.toCategoryStruct
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
CompleteBooleanAlgebra.toCompleteLattice
CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra
IsOpenImmersion
Surjective
CategoryTheory.MorphismProperty.ext
CategoryTheory.MorphismProperty.isomorphisms.iff
isIso_iff_isOpenImmersion_and_surjective
isomorphisms_eq_stalkwise 📖mathematicalCategoryTheory.MorphismProperty.isomorphisms
Scheme
Scheme.instCategory
CategoryTheory.MorphismProperty
CategoryTheory.Category.toCategoryStruct
SemilatticeInf.toMin
Lattice.toSemilatticeInf
ConditionallyCompleteLattice.toLattice
CompleteLattice.toConditionallyCompleteLattice
CompleteBooleanAlgebra.toCompleteLattice
CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra
CategoryTheory.MorphismProperty.inverseImage
TopCat
TopCat.instCategory
Scheme.forgetToTop
stalkwise
Function.Bijective
DFunLike.coe
RingHom
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
RingHom.instFunLike
isomorphisms_eq_isOpenImmersion_inf_surjective
isOpenImmersion_eq_inf
surjective_eq_topologically
inf_right_comm
CategoryTheory.MorphismProperty.ext
Topology.IsOpenEmbedding.toIsEmbedding
CategoryTheory.Iso.isIso_hom
Homeomorph.isOpenEmbedding
Homeomorph.surjective

CategoryTheory

Definitions

NameCategoryTheorems
IsIso 📖CompData
767 mathmath: FinitaryPreExtensive.isIso_sigmaDesc_fst, GrothendieckTopology.W_sheafToPresheaf_map_iff_isIso, Adjunction.Triple.isIso_unit_iff_isIso_counit, Functor.IsDenseSubsite.instIsIsoSheafAppCounitSheafAdjunctionCocontinuous, Limits.coequalizer.π_of_self, Functor.isLeftKanExtension_iff_isIso, isIso_of_op, Grp.instIsIsoHomHomMon, isIso_sheafificationAdjunction_counit, Functor.isIso_of_isRightDerivedFunctor_of_inverts, Monad.algebra_iso_of_iso, Limits.image.isIso_precomp_iso, ComplexShape.Embedding.isIso_liftExtend_f_iff, AlgebraicGeometry.IsClosedImmersion.instIsIsoSchemeToImage, conjugateEquiv_iso, ShortComplex.HomologyData.ofIso_right_p, HomotopicalAlgebra.FibrantObject.instIsIsoFunctorWhiskerRightHoCatιCompResolutionNatTransOfIsLocalizationWeakEquivalences, Limits.isIso_ι_terminal, Limits.equalizer.ι_of_eq, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.stalk_iso, NatTrans.isIso_app_iff_of_iso, Limits.CategoricalPullback.instIsIsoSnd, ShortComplex.isIso_leftHomologyπ, Functor.instIsIsoAppCounitRanAdjunctionOfHasPointwiseRightKanExtension, isIso_of_yoneda_map_bijective, isIso_homOfLE, Limits.colimitLimitToLimitColimit_isIso, Limits.isIso_prod, Limits.isIso_cokernel_map_of_isPushout, isIso_of_fully_faithful, Limits.isIso_app_coconePt_of_preservesColimit, ComposableArrows.isIso_iff₂, AlgebraicGeometry.instIsIsoSchemeCoprodComparisonOppositeCommRingCatSpec, CondensedMod.IsSolid.isIso_solidification_map, AlgebraicGeometry.ΓSpec.isIso_adjunction_counit, isIso_of_coyoneda_map_bijective, MorphismProperty.isIso_fst'_self, ShortComplex.quasiIso_iff_isIso_rightHomologyMap', ShortComplex.isIso_homologyFunctor_map_of_epi_of_isIso_of_mono, Adjunction.instIsIsoAppUnitObjOfFaithfulOfFull, AlgebraicGeometry.Scheme.Hom.exists_isIso_morphismRestrict_toNormalization, prodComparison_iso, MonoOver.isIso_left_iff_subobjectMk_eq, Pretriangulated.Triangle.instIsIsoHom₂, AlgebraicGeometry.isIso_SpecMap_iff, NatIso.isIso_app_of_isIso, ShortComplex.isIso_homologyMap_of_isIso_cyclesMap_of_epi, Adjunction.instIsIsoFunctorCounitOfIsEquivalence_1, Functor.instIsIsoAppRanCounit, Adjunction.instIsIsoAppCounitOfFullOfFaithful, MonoidalCategory.MonoidalLeftAction.isIso_actionHom, to_initial_isIso, isIso_unop_iff, Functor.Monoidal.instIsIsoδ, CondensedMod.isDiscrete_tfae, MonoOver.isIso_iff_subobjectMk_eq, Functor.IsEventuallyConstantFrom.isIso_ι_of_isColimit', Functor.LeftLinear.instIsIsoδₗ, AlgebraicGeometry.Scheme.Cover.instIsIsoFromGlued, Limits.Cocones.cocone_iso_of_hom_iso, AlgebraicGeometry.instIsIsoSchemeSigmaSpecOfFinite, SSet.Truncated.sk_coreflective, AlgebraicTopology.DoldKan.instIsIsoFunctorSimplicialObjectKaroubiNatTrans, IsIso.of_epi_section, isIso_of_reflects_iso, Functor.instIsIsoAppUnitLanAdjunctionOfHasPointwiseLeftKanExtension, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.instIsIsoInvApp, Limits.pushout_inr_iso_of_left_iso, ShortComplex.isIso_iCycles, AlgebraicGeometry.Scheme.Hom.instIsIsoToNormalizationOfIsIntegralHom, Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.isIso_hom_app, AlgebraicGeometry.isIso_ΓSpec_adjunction_unit_app_basicOpen, ObjectProperty.IsStrongGenerator.isIso_of_mono, IsSubterminal.isIso_diag, ShortComplex.exact_iff_isIso_imageToKernel', Arrow.isIso_of_isIso_left_of_isIso_right, instIsIsoFunctorOppositeValAppSheafCounitSheafificationAdjunction, Limits.pullback_snd_iso_of_left_iso, MorphismProperty.isomorphisms.iff, Limits.instIsIsoPushoutComparison, ShortComplex.isIso_homologyπ, Subobject.top_arrow_isIso, Functor.Monoidal.instIsIsoη, CondensedSet.instIsIsoFunctorCompactlyGeneratedCounitCompactlyGeneratedAdjunction, Functor.reflective', Comma.instIsIsoRight, IsIso.of_mono_retraction', isIso_of_isDiscrete, Adjunction.instIsIsoFunctorUnitOfIsEquivalence, LightCondMod.isDiscrete_tfae, Presheaf.isLeftKanExtension_along_yoneda_iff, ShortComplex.isIso_cyclesMap'_of_isIso_of_mono, IsPushout.isIso_inr_of_isIso, CompHausLike.isIso_of_bijective, StrictlyUnitaryLaxFunctor.mapId_isIso, IsHomLift.isIso_of_lift_isIso, ShortComplex.isIso_leftRightHomologyComparison, Limits.Cofan.isColimit_iff_isIso_sigmaDesc, IsIso.of_isIso_comp_left, ShortComplex.isIso_leftHomologyMap'_of_isIso, CochainComplex.instIsIsoIntπTruncGEOfIsStrictlyGE, ShortComplex.isIso_cyclesMap_of_isIso_of_mono, AlgebraicGeometry.IsOpenImmersion.iff_isIso_stalkMap, AlgebraicGeometry.Scheme.Cover.instIsIsoCommRingCatStalkMapFromGlued, IsSifted.instIsIsoObjFunctorTypeColimTensorObjProdComparison, IsIso.instUnmopOfMonoidalOpposite, Presheaf.isIso_of_isLeftKanExtension, GrothendieckTopology.isIso_toSheafify, isIso_comp_right_iff, Limits.instIsIsoHomHomCocone, Limits.IsInitial.isIso_to, NonPreadditiveAbelian.isIso_factorThruCoimage, instIsIsoToRightDerivedZero', Monad.isSplitMono_iff_isIso_unit, isIso_iff_coyoneda_map_bijective, Adjunction.instIsIsoAppCounitObjOfFaithfulOfFull, Functor.isRightDerivedFunctor_iff_of_inverts, MonoidalCategory.MonoidalRightAction.isIso_actionHom, PreZeroHypercover.instIsIsoH₀Hom, ShortComplex.isIso_opcyclesMap'_of_isIso, ShortComplex.LeftHomologyData.isIso_i, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.stalk_iso, AlgebraicGeometry.Scheme.Modules.instIsIsoFunctorCounitRestrictAdjunction, Functor.ReflectsIsomorphisms.reflects, MonoidalClosedFunctor.comparison_iso, AlgebraicTopology.DoldKan.instIsIsoFunctorKaroubiSimplicialObjectNatTrans, ShortComplex.ShortExact.isIso_g_iff, isIso_of_epi_of_strongMono, ShortComplex.isIso₂_of_shortExact_of_isIso₁₃', LocalizerMorphism.Derives.isIso, isIso_toSheafify, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.isIso_of_subset, Limits.IsLimit.nonempty_isLimit_iff_isIso_lift, MonoOver.isIso_hom_left_iff_subobjectMk_eq, AlgebraicGeometry.isIso_iff_isIso_stalkMap, MonoidalCategory.MonoidalLeftAction.isIso_actionHomLeft, Functor.isIso_whiskerRight, Limits.kernelSubobject_comp_mono_isIso, Limits.CategoricalPullback.isIso_iff, ShortComplex.RightHomologyMapData.quasiIso_map_iff, Limits.pullback.instIsIsoDiagonalOfMono, ShortComplex.isIso_leftRightHomologyComparison', Limits.isIso_of_isTerminal, Limits.HasZeroObject.zero_to_zero_isIso, HomologicalComplex.instIsIsoFRestrictionToTruncGE'OfIsStrictlySupported, Limits.instIsIsoTerminalComparison, Limits.IsColimit.nonempty_isColimit_iff_isIso_desc, Presheaf.instIsIsoFunctorOfIsLeftKanExtensionOppositeType, Profinite.isIso_indexCone_lift, Limits.cokernel.π_zero_isIso, Limits.isIso_of_isInitial, Pretriangulated.Triangle.distinguished_iff_of_isZero₃, GradedObject.isIso_apply_of_isIso, TopCat.isIso_iff_isHomeomorph, Limits.instIsIsoMapOfMono, LightCondSet.instIsIsoFunctorSequentialCounitSequentialAdjunction, Sheaf.instIsIsoAppCounitConstantSheafAdjOfFaithfulOfFullConstantSheafOfIsConstant, Limits.isIsoZero_iff_source_target_isZero, TopCat.fst_iso_of_right_embedding_range_subset, Limits.CatCospanTransform.instIsIsoWhiskerLeft, HomotopicalAlgebra.BifibrantObject.instIsIsoHoCatMapToHoCatOfWeakEquivalence, GrothendieckTopology.preservesSheafification_iff_of_adjunctions, Limits.CokernelCofork.IsColimit.isIso_π, MorphismProperty.TransfiniteCompositionOfShape.isIso, CommGrp.instIsIsoMonHomGrp, instIsIsoFunctorOppositeSheafSheafComposeNatTrans, ShortComplex.Exact.isIso_imageToKernel, AlgebraicGeometry.Scheme.Hom.isIso_base, ShortComplex.isIso_pOpcycles, AlgebraicGeometry.IsOpenImmersion.isIso, AlgebraicGeometry.isIso_morphismRestrict_iff_isIso_app, isIso_iff_bijective, ShortComplex.exact_iff_isIso_imageToKernel, isIso_pi_iff, CommMon.instIsIsoHomHomMon, isIso_of_regularEpi_of_mono, Adjunction.instIsIsoFunctorCounitOfIsEquivalence, TopCat.GlueData.instIsIsoT, Pretriangulated.Triangle.distinguished_iff_of_isZero₁, IsGrothendieckAbelian.exists_isIso_of_functor_from_monoOver, GrothendieckTopology.W_iff_isIso_map_of_adjunction, Comonad.isSplitEpi_iff_isIso_counit, isIso_of_mono_of_nonzero, Limits.IsColimit.isIso_colimMap_ι, GlueData.f_id, ExtremalEpi.isIso, InjectiveResolution.instIsIsoToRightDerivedZero'Self, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.to_iso, Action.isIso_of_hom_isIso, SimplexCategory.isIso_iff_of_epi, Limits.IsIPC.isIso, IsIso.inv_isIso, Bicategory.conjugateEquiv_symm_of_iso, Pretriangulated.Triangle.isIso_of_isIsos, instIsIsoAppToRightDerivedZeroOfInjective, ShortComplex.QuasiIso.isIso, ShortComplex.quasiIso_iff_isIso_homologyMap', Limits.isIso_limit_cone_parallelPair_of_epi, Adjunction.isIso_counit_of_iso, isIso_comp_left_iff, FinitaryPreExtensive.isIso_sigmaDesc_map, isIso_right_of_isIso_biprod_map, Limits.HasStrictTerminalObjects.out, Functor.instIsIsoAppLanUnit, SSet.S.mk_map_eq_iff_of_mono, isUnit_iff_isIso, Limits.HasStrictInitialObjects.out, Bicategory.instIsIsoHomLeftZigzagHom, AlgebraicGeometry.Spec_map_localization_isIso, Pseudofunctor.DescentData.instIsIsoαCategoryObjLocallyDiscreteOppositeCatMkOpHom, HomologicalComplex.isIso_homologyπ, ShortComplex.instIsIsoτ₃, TwoSquare.isIso_lanBaseChange_app, Adjunction.isIso_counit_app_of_iso, SimplexCategory.isIso_of_bijective, conjugateEquiv_symm_iso, ObjectProperty.isLocal_iff_isIso, IsGrothendieckAbelian.IsPresentable.surjectivity.isIso_f, Endofunctor.Algebra.Initial.str_isIso, Limits.CatCospanTransform.instIsIsoWhiskerRight, ShortComplex.instIsIsoτ₁, Pretriangulated.Triangle.distinguished_iff_of_isZero₂, Action.instIsIsoHomInv, ShortComplex.isIso_leftRightHomologyComparison'_of_homologyData, Adjunction.instIsIsoAppUnitOfFullOfFaithful, DerivedCategory.instIsIsoMapCochainComplexIntQ, HomologicalComplex.isIso_homologyMap_shortComplexTruncLE_g, CochainComplex.isIso_πTruncGE_iff, AlgebraicGeometry.isIso_stalkMap_coprodSpec, AlgebraicGeometry.PresheafedSpace.isIso_of_components, SimplexCategory.isIso_iff_of_mono, isIso_iff_isIso_yoneda_map, ShortComplex.quasiIso_iff_isIso_descOpcycles, isIso_of_hom_simple, Functor.essImage.counit_isIso, SSet.isIso_of_nonDegenerate, Limits.PullbackCone.isIso_fst_of_mono_of_isLimit, GradedObject.instIsIsoMapBifunctorMapMap, AlgebraicGeometry.Scheme.instIsIsoCommRingCatResidueFieldMapOfIsOpenImmersion, Comonad.coalgebra_iso_of_iso, isIso_op, Subobject.isIso_top_arrow, MorphismProperty.TransfiniteCompositionOfShape.instIsIsoAppIncl, GrothendieckTopology.instIsIsoFunctorOppositeSheafSheafComposeNatTransPlusPlusAdjunction, Limits.CatCospanTransform.isIso_base, AlgebraicGeometry.isIso_pushoutSection_of_isCompact_of_flat_right_of_ringHomFlat, AlgebraicGeometry.Scheme.Hom.isIso_toLRSHom, Functor.isLeftDerivedFunctor_iff_of_inverts, OverClass.instIsIsoOverAsOverHom, HomologicalComplex.instIsIsoπTruncGEOfIsStrictlySupported, ProjectiveResolution.instIsIsoFromLeftDerivedZero'Self, Adjunction.whiskerRight_counit_iso_of_L_fully_faithful, ShortComplex.QuasiIso.isIso', FundamentalGroupoidFunctor.instIsIsoFanGrpdObjTopCatFundamentalGroupoidFunctorPiTopToPiCone, IsIso.of_isIso_comp_right, Bicategory.whiskerLeft_isIso, ShortComplex.isIso_cyclesMap_of_isIso_of_mono', AlgebraicGeometry.IsOpenImmersion.to_iso, AlgebraicGeometry.PresheafedSpace.ofRestrict_stalkMap_isIso, Adjunction.instIsIsoFunctorUnitOfIsEquivalence_1, AlgebraicGeometry.instIsIsoSchemeMorphismRestrict, Functor.isIso_ranAdjunction_unit_app_iff, Pretriangulated.isIso₃_of_isIso₁₂, Limits.BinaryCofan.isColimit_iff_isIso_inl, Limits.cokernel.π_of_zero, Functor.final_iff_isIso_colimit_pre, Limits.CategoricalPullback.instIsIsoFst, instIsIsoAppFromLeftDerivedZeroOfProjective, Adjunction.isIso_unit_app_iff_mem_essImage, Pretriangulated.Triangle.isZero₂_iff_isIso₃, ShortComplex.LeftHomologyMapData.quasiIso_map_iff, AlgebraicGeometry.isIso_iff_isOpenImmersion_and_surjective, ObjectProperty.isColocal_iff_isIso, Pretriangulated.Triangle.isZero₃_iff_isIso₁, IsIso.comp_isIso, AlgebraicGeometry.AffineSpace.instIsIsoSchemeOverInferInstanceOverClassOfIsEmpty, ShortComplex.instIsIsoLeftHomologyMapOfEpiτ₁Ofτ₂OfMonoτ₃, AlgebraicGeometry.Scheme.Hom.instIsIsoNormalizationPullbackOfSmooth, IsIso.of_isIso_fac_right, ChainComplex.isIso_descOpcycles_iff, AlgebraicGeometry.isIso_iff_isOpenImmersion, Limits.KernelFork.IsLimit.isIso_ι, Subfunctor.eq_top_iff_isIso, Abelian.OfCoimageImageComparisonIsIso.instIsIsoEImageMonoFactorisationOfHasZeroObjectOfMonoOfCoimageImageComparison, Functor.OplaxMonoidal.instIsIsoη, IsPullback.isIso_snd_iso_of_mono, instIsIsoIndCoimageImageComparison, NatTrans.isIso_iff_isIso_app, FundamentalGroupoidFunctor.instIsIsoFunctorFundamentalGroupoidHomotopicMapsNatIso, Limits.instIsIsoEqualizerComparison, Limits.kernel.ι_of_zero, Limits.PushoutCocone.isIso_inl_of_epi_of_isColimit, Functor.Monoidal.instIsIsoμ, NonPreadditiveAbelian.isIso_r, instIsIsoHomologyMapOfQuasiIsoAt, Pretriangulated.Triangle.instIsIsoHom₃, ComposableArrows.Exact.isIso_map', Presheaf.isLeftKanExtension_along_uliftYoneda_iff, Limits.BinaryCofan.isColimit_iff_isIso_inr, Functor.IsEventuallyConstantTo.isIso_map, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.to_iso, Limits.instIsIsoKernelComparison, AlgebraicGeometry.isOpenImmersion_iff_stalk, AlgebraicGeometry.tilde.isIso_toOpen_top, Limits.IsTerminal.isIso_from, Functor.IsStronglyCartesian.isIso_of_base_isIso, strict_initial, Arrow.isIso_left, Arrow.isIso_hom_iff_isIso_of_isIso, Limits.pushout_inr_iso_of_right_factors_epi, IsIso.of_isIso_fac_left, AlgebraicGeometry.isIso_of_comp_eq_sigmaSpec, instIsIsoEqToHom, Limits.isIso_colimit_cocone_parallelPair_of_eq, isIso_of_comp_hom_eq_id, PreGaloisCategory.FibreFunctor.end_isIso, AlgebraicGeometry.PresheafedSpace.stalkMap.isIso, IsGroupoid.all_isIso, HomologicalComplex.isIso_ιTruncLE_iff, conjugateEquiv_symm_of_iso, TwoSquare.isIso_lanBaseChange_app_iff, TwoSquare.instIsIsoFunctorLanBaseChangeOfGuitartExact, isIso_iff_nonzero, AlgebraicGeometry.instIsIsoSchemeAppUnitOppositeCommRingCatAdjunctionOfIsAffine, SmallObject.instIsIsoRightAppArrowMapToTypeOrdFunctorIterationFunctor, Discrete.instIsIso, frobeniusMorphism_iso_of_preserves_binary_products, Limits.instIsIsoProdComparison, Abelian.isIso_of_epi_of_isIso_of_isIso_of_mono, ShortComplex.isIso_homologyι, ShortComplex.SnakeInput.isIso_δ, AlgebraicGeometry.ΓSpec.isIso_locallyRingedSpaceAdjunction_counit, IsPushout.isIso_inr_iso_of_epi, Pretriangulated.isIso₂_of_isIso₁₃, SimplicialObject.instIsIsoAppUnitTruncatedCoskAdj, Arrow.isIso_iff_isIso_of_isIso, Functor.RightExtension.IsPointwiseRightKanExtension.isIso_hom, PreGaloisCategory.isIso_of_mono_of_eq_card_fiber, Functor.isIso_ranAdjunction_homEquiv_iff, Functor.isIso_of_isLeftDerivedFunctor_of_inverts, Functor.essImage.unit_isIso, IsPullback.isIso_snd_of_isIso, AlgebraicGeometry.isIso_of_isEmpty, HomologicalComplex.isIso_truncLE'ToRestriction, Limits.instIsIsoCoprodComparison, HomotopicalAlgebra.CofibrantObject.instIsIsoFunctorWhiskerRightHoCatιCompResolutionNatTransOfIsLocalizationWeakEquivalences, AlgebraicGeometry.PresheafedSpace.base_isIso_of_iso, BasedNatIso.isIso_of_toNatTrans_isIso, isIso_of_mono_of_strongEpi, isIso_left_of_isIso_biprod_map, Limits.Cocone.isColimit_iff_isIso_colimMap_ι, Presheaf.isSheaf_iff_multiequalizer, HomotopicalAlgebra.CofibrantObject.instIsIsoFunctorHoCatAdjCounit', Adjunction.whiskerLeft_counit_iso_of_L_fully_faithful, Endofunctor.Coalgebra.iso_of_iso, ShortComplex.isIso_of_isIso, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.instIsIsoCommRingCatInvApp, HomotopicalAlgebra.CofibrantObject.instIsIsoFunctorHoCatCounitHoCatAdj, Limits.instIsIsoHomInvCone, Functor.RightLinear.instIsIsoμᵣ, Iso.isIso_inv, Limits.instIsIsoCokernelComparison, AlgebraicGeometry.Scheme.Modules.Hom.isIso_iff_isIso_app, Adjunction.unit_isIso_of_L_fully_faithful, HomologicalComplex.isIso_iCycles, HomotopicalAlgebra.CofibrantObject.instIsIsoFunctorResolutionCompToLocalizationNatTrans, ObjectProperty.isStrongGenerator_iff, instIsIsoAppUnitReflectorAdjunctionObjEssImage, CartesianMonoidalCategory.terminalComparison_isIso_of_preservesLimits, Functor.RightLinear.instIsIsoδᵣ, AlgebraicGeometry.PresheafedSpace.GlueData.componentwise_diagram_π_isIso, TopCat.isIso_of_bijective_of_isOpenMap, TopCat.snd_iso_of_left_embedding_range_subset, AlgebraicGeometry.isIso_iff_isOpenImmersion_and_epi_base, Sheaf.isConstant_iff_isIso_counit_app', CochainComplex.isIso_liftCycles_iff, Limits.isIso_fst_of_mono, Limits.isIso_limit_cone_parallelPair_of_eq, AlgebraicGeometry.IsAffineOpen.basicOpenSectionsToAffine_isIso, isIso_unop, Iso.isIso_hom, Limits.pullback_snd_iso_of_left_factors_mono, Functor.RightExtension.IsPointwiseRightKanExtensionAt.isIso_hom_app, HomologicalComplex.isIso_πTruncGE_iff, ShortComplex.instIsIsoRightHomologyMap'OfEpiτ₁Ofτ₂OfMonoτ₃, ShortComplex.ShortExact.isIso_δ, PartialOrder.isIso_iff_eq, Coreflective.instIsIsoAppCounitCoreflectorAdjunctionA, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_isIso, AlgebraicGeometry.PresheafedSpace.c_isIso_of_iso, GrothendieckTopology.Point.instIsIsoMapFunctorOppositePresheafFiberToSheafify, MonoidalCategory.whiskerRight_isIso, regularTopology.equalizerCondition_iff_isIso_lift, LightCondMod.LocallyConstant.instIsIsoLightCondSetMapForgetAppLightCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, GrothendieckTopology.preservesSheafification_iff_of_adjunctions_of_hasSheafCompose, AlgebraicGeometry.LocallyRingedSpace.ofRestrict_stalkMap_isIso, Limits.pushout_inl_iso_of_left_factors_epi, Simple.mono_isIso_iff_nonzero, Action.instIsIsoHomHom, Pretriangulated.Triangle.instIsIsoHom₁, ShortComplex.isIso_rightHomologyMap_of_iso, PreZeroHypercover.instIsIsoH₀Inv, Monoidal.Reflective.instIsIsoAppUnitObjIhom, Subfunctor.instIsIsoFunctorTypeιTop, Functor.isIso_lanAdjunction_homEquiv_symm_iff, ShortComplex.isIso_rightHomologyMap'_of_isIso, Limits.colimitLimitToLimitColimitCone_iso, Functor.LeftExtension.IsPointwiseLeftKanExtension.isIso_hom, Subfunctor.instIsIsoFunctorTypeToRangeOfMono, Subobject.mk_lt_mk_iff_of_comm, Endofunctor.Coalgebra.Terminal.str_isIso, hoFunctor.isIso_prodComparison_stdSimplex, AlgebraicGeometry.IsClosedImmersion.isIso_lift, instIsIsoOverInferInstanceOverClass, Limits.instIsIsoEqToHom, isIso_iff_of_reflects_iso, AlgebraicGeometry.Scheme.Modules.instIsIsoAbApp, MorphismProperty.TransfiniteCompositionOfShape.instIsIsoMapF, Abelian.OfCoimageImageComparisonIsIso.instIsIsoMImageMonoFactorisationOfHasZeroObjectOfEpi, Balanced.isIso_of_mono_of_epi, ShortComplex.isIso_rightHomologyι, NatIso.hom_app_isIso, Limits.IsLimit.isIso_limMap_π, Limits.kernel.ι_zero_isIso, AlgebraicGeometry.Scheme.Hom.isIso_app, MonoOver.isIso_iff_isIso_hom_left, AlgebraicGeometry.Scheme.LocalRepresentability.instIsIsoSheafZariskiTopologyTypeYonedaGluedToSheaf, Adjunction.isIso_unit_of_iso, Coyoneda.isIso, ShortComplex.ShortExact.isIso_f_iff, ObjectProperty.IsDetecting.isIso_iff_of_mono, AlgebraicGeometry.Scheme.Hom.exists_mem_and_isIso_morphismRestrict_toNormalization, Arrow.isIso_hom_iff_isIso_hom_of_isIso, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.to_iso, ShortComplex.Exact.isIso_g', Limits.instIsIsoSigmaComparison, CochainComplex.instIsIsoIntιTruncLEOfIsStrictlyLE, ConcreteCategory.isIso_iff_bijective, quasiIsoAt_iff_isIso_homologyMap, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullback_snd_isIso_of_range_subset, isIso_iff_mono_and_epi, ShortComplex.isIso_homologyMap'_of_epi_of_isIso_of_mono, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.c_iso, ObjectProperty.isColocal_iff_isIso_map, AlgebraicGeometry.IsClosedImmersion.isIso_of_ker_eq, AlgebraicGeometry.IsOpenImmersion.instIsIsoCommRingCatStalkMap, Functor.IsEventuallyConstantTo.isIso_π_of_isLimit, AlgebraicGeometry.Scheme.instIsIsoSubschemeιBotIdealSheafData, Cat.Hom.instIsIsoFunctorαCategoryToNatTransInvHom, HomotopyCategory.mem_quasiIso_iff, Limits.isIso_kernelSubobject_zero_arrow, ShortComplex.instIsIsoτ₂, Arrow.isIso_of_isIso, IsPullback.isIso_fst_of_mono, CondensedSet.isDiscrete_tfae, Limits.instIsIsoPullbackComparison, Limits.CatCospanTransform.isIso_left, AlgebraicGeometry.ProjectiveSpectrum.Proj.isIso_toSpec, PreGaloisCategory.IsConnected.noTrivialComponent, TopCat.isIso_of_bijective_of_isClosedMap, IsDetecting.isIso_iff_of_mono, AlgebraicGeometry.Scheme.Hom.instIsIsoCommRingCatAppObjOpensOpensFunctor, instIsIsoAppToRightDerivedZero, ShortComplex.isIso_homologyMap_of_isIso, Limits.pullback.isIso_diagonal_iff, localization_unit_isIso, Adjunction.counit_isIso_of_R_fully_faithful, ShortComplex.isIso₂_of_shortExact_of_isIso₁₃, Functor.IsCoverDense.iso_of_restrict_iso, MonoidalCategory.MonoidalRightAction.isIso_actionHomLeft, MorphismProperty.LeftFraction.Localization.instIsIsoQinv, isIso_of_mono_of_isSplitEpi, ShortComplex.RightHomologyData.isIso_ι, Limits.BinaryFan.isLimit_iff_isIso_fst, HomologicalComplex.isIso_pOpcycles, Functor.relativelyRepresentable.instIsIsoSymmetryOfFaithful, MorphismProperty.Comma.instIsIsoCommaHom, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓUnitOpensCarrierCarrierCommRingCatRingCatSheaf, Bicategory.conjugateEquiv_of_iso, Limits.instIsIsoInitialComparison, instIsIsoPost_1, Limits.kernel.of_cokernel_of_epi, GlueData.t_isIso, Limits.biprod.isIso_inl_iff_id_eq_fst_comp_inl, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.c_iso', AlgebraicGeometry.SheafedSpace.IsOpenImmersion.stalk_iso, Localization.LeftBousfield.W_iff_isIso, ComposableArrows.instIsIsoOfNatNatTwoδ₁Toδ₀, LocalizerMorphism.isIso_iff_of_hasRightResolutions, OrthogonalReflection.isIso_toSucc_iff, ShortComplex.Exact.isIso_f', AlgebraicGeometry.isIso_of_isClosedImmersion_of_surjective, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, instIsIsoFunctorToRightDerivedZero, Functor.reflective, CommGrp.instIsIsoGrpHom, ShortComplex.isIso_opcyclesMap_of_iso, IsCodetecting.isIso_iff_of_epi, ChainComplex.isIso_homologyι₀, Biprod.isIso_inl_iff_isZero, ObjectProperty.isLocal_iff_isIso_map, ShortComplex.instIsIsoLeftHomologyMap'OfEpiτ₁Ofτ₂OfMonoτ₃, isCodetector_def, ShortComplex.quasiIso_iff, Adjunction.instIsIsoMapAppUnitOfFaithfulOfFull, ComposableArrows.isIso_iff₀, ShortComplex.RightHomologyData.isIso_p, HomotopicalAlgebra.CofibrantObject.instIsIsoHoCatAppAdjCounit', Limits.pullback_snd_iso_of_right_factors_mono, SimplicialObject.Truncated.cosk_reflective, Functor.Final.colimit_pre_isIso, isIso_of_regularMono_of_epi, ShortComplex.isIso_opcyclesMap'_of_isIso_of_epi, AlgebraicGeometry.isIso_SpecMap_stakMap_localization, Functor.FullyFaithful.isIso_of_isIso_map, Functor.Monoidal.instIsIsoε, Limits.pushout_inl_iso_of_right_iso, IsIso.of_mono_retraction, Limits.Cone.isLimit_iff_isIso_limMap_π, expComparison_iso_of_frobeniusMorphism_iso, Limits.terminal_isIso_from, isIso_iff_yoneda_map_bijective, CompHausLike.LocallyConstant.instIsIsoFunctorTypeUnitSheafCoherentTopologyAdjunction, Subobject.isIso_arrow_iff_eq_top, instIsIsoAppFromLeftDerivedZero, IsCodetector.def, Sieve.functorInclusion_top_isIso, AlgebraicGeometry.IsOpenImmersion.iff_stalk_iso, Limits.equalizer.ι_of_self, Bicategory.conjugateEquiv_symm_iso, CompHausLike.isIsoSigmaComparison, HomologicalComplex.instIsIsoFTruncLE'ToRestrictionOfIsStrictlySupported, Functor.IsRepresentedBy.iff_isIso_uliftYonedaEquiv, NatIso.isIso_map_iff, ShortComplex.isIso_opcyclesMap_of_isIso_of_epi', isIso_of_epi_of_nonzero, Bicategory.instIsIsoHomRightZigzagHom, ShortComplex.isIso_leftHomologyMap_of_iso, SheafOfModules.instIsIsoPullbackObjUnitToUnitOfFinal, GrothendieckTopology.W_iff, Endofunctor.Algebra.iso_of_iso, NatIso.inv_app_isIso, δ_iso_of_coreflective, PrelaxFunctor.map₂_isIso, LightProfinite.isIso_of_bijective, ShortComplex.isIso_homologyMap_of_isIso_opcyclesMap_of_mono, SimplicialObject.Truncated.sk_coreflective, AlgebraicGeometry.IsAffine.affine, Functor.map_isIso, IsKernelPair.isIso_of_mono, Limits.initial_isIso_to, isIso_of_mono_of_epi, Limits.IsColimit.hom_isIso, ShortComplex.LeftHomologyData.isIso_π, ShortComplex.isIso_homologyMap_of_iso, Limits.Cones.instIsIsoConeExtend, Sheaf.isLocallyBijective_iff_isIso, AlgebraicGeometry.LocallyRingedSpace.is_sheafedSpace_iso, Functor.isRightDerivedFunctor_iff_isIso_rightDerivedDesc, HomologicalComplex.instIsIsoιTruncLEOfIsStrictlySupported, Limits.isIso_π_of_isInitial, instIsIsoFunctorOppositeSheafToPresheafToSheafCompComposeAndSheafify, Functor.isRightKanExtension_iff_isIso, Limits.Fan.nonempty_isLimit_iff_isIso_piLift, AlgebraicGeometry.isIso_pushoutSection_of_isQuasiSeparated_of_flat_left, ComposableArrows.Exact.isIso_cokerToKer', JointlyReflectIsomorphisms.isIso_iff, AlgebraicGeometry.isIso_pushoutSection_iff, isIso_iff_isIso_coyoneda_map, Limits.isIso_of_source_target_iso_zero, HomotopicalAlgebra.FibrantObject.instIsIsoFunctorResolutionCompToLocalizationNatTrans, hoFunctor.instIsIsoCatProdComparisonSSetHoFunctorNerve, ShortComplex.LeftHomologyMapData.quasiIso_iff, Limits.instIsIsoCoequalizerComparison, Limits.IsColimit.isIso_ι_app_of_isTerminal, Adjunction.isIso_unit_app_of_iso, AlgebraicGeometry.isIso_iff_stalk_iso, SSet.Truncated.cosk_reflective, LocalizerMorphism.Derives.isRightDerivedFunctor_iff_isIso, LocalizerMorphism.isIso_iff_of_isRightDerivabilityStructure, instIsIsoFunctorFromLeftDerivedZero, AlgebraicGeometry.Scheme.Hom.isIso_toPshHom, CochainComplex.isIso_ιTruncLE_iff, Subobject.isIso_iff_mk_eq_top, AlgebraicGeometry.Flat.isIso_of_surjective_of_mono, Bicategory.whiskerRight_isIso, MorphismProperty.Comma.instIsIsoHomFromCommaOfIsIso, μ_iso_of_reflective, Limits.instIsIsoPiComparison, Limits.PullbackCone.isIso_snd_of_mono_of_isLimit, groupHomology.isIso_δ_of_isZero, AlgebraicGeometry.instHasAffinePropertyIsomorphismsSchemeAndIsAffineIsIsoCommRingCatAppTop, homOfLE_isIso_of_eq, HomologicalComplex.isIso_restrictionToTruncGE', LightCondSet.isDiscrete_tfae, epi_iff_isIso_inl, AlgebraicGeometry.instIsIsoSchemeCoprodSpec, frobeniusMorphism_iso_of_expComparison_iso, isIso_of_epi_of_isSplitMono, Limits.limit_π_isIso_of_is_strict_terminal, BasedNatTrans.instIsIsoFunctorObjOfBasedFunctor, Limits.isIso_inr_of_epi, IsDetector.def, Functor.IsEventuallyConstantFrom.isIso_map, Functor.isIso_whiskerLeft, ShortComplex.isIso_homologyMap_of_epi_of_isIso_of_mono', Abelian.FunctorCategory.functor_category_isIso_coimageImageComparison, SingleFunctors.instIsIsoFunctorHom, ShortComplex.isIso_homologyMap_of_epi_of_isIso_of_mono, Functor.instIsIsoAppLanUnit_1, IsIso.of_epi_section', Limits.isIso_coprod, Limits.Cofan.nonempty_isColimit_iff_isIso_sigmaDesc, ShortComplex.isIso_cyclesMap'_of_isIso, AlgebraicGeometry.Scheme.Hom.instIsIsoCommRingCatApp, hom_isIso, Comma.instIsIsoLeft, GrothendieckTopology.instIsIsoSheafAppFunctorOppositeSheafComposeNatTransPlusPlusAdjunction, ShortComplex.isIso_opcyclesMap_of_isIso_of_epi, Mon.instIsIsoHom, ShortComplex.quasiIso_iff_isIso_leftHomologyMap', Functor.IsEventuallyConstantTo.isIso_π_of_isLimit', Functor.IsStronglyCocartesian.isIso_of_base_isIso, IsIso.of_groupoid, Sieve.uliftFunctorInclusion_top_isIso, ShortComplex.isIso_homologyMap'_of_isIso, Abelian.isIso_factorThruImage, localization_unit_isIso', NonPreadditiveAbelian.isIso_factorThruImage, ProfiniteGrp.isIso_toLimit, SimplicialObject.isCoskeletal_iff_isIso, Functor.LeftLinear.instIsIsoμₗ, AlgebraicGeometry.SheafedSpace.is_presheafedSpace_iso, ShortComplex.isIso_cyclesMap_of_iso, IsPullback.isIso_fst_of_isIso, Limits.isIso_π_initial, GlueData.t'_isIso, IsIso.comp_isIso', Limits.instIsIsoHomInvCocone, Limits.isIso_kernel_map_of_isPullback, AlgebraicGeometry.Scheme.Opens.instIsIsoCommRingCatAppLEιTopToScheme, Limits.isIso_colimit_cocone_parallelPair_of_self, MonoidalCategory.tensor_isIso, Limits.instIsIsoDescι, Functor.coreflective', Functor.IsEventuallyConstantFrom.isIso_ι_of_isColimit, sheafification_reflective, AlgebraicGeometry.instIsIsoFunctorModuleCatCarrierUnitModulesSpecOfAdjunction, Comon.instIsIsoHomOfMapForget, Limits.pullback_fst_iso_of_right_iso, AlgebraicGeometry.isIso_of_isOpenImmersion_of_opensRange_eq_top, Center.isIso_of_f_isIso, Limits.isIso_snd_of_mono, AlgebraicGeometry.instIsIsoSchemeMapOfCommRingCat, AlgebraicGeometry.isIso_pushoutSection_of_isQuasiSeparated_of_flat_right, conjugateEquiv_of_iso, mono_iff_isIso_fst, ComposableArrows.instIsIsoOfNatNatTwoδ₂Toδ₁, RelCat.rel_iso_iff, AlgebraicGeometry.isIso_toSpecΓ, Adjunction.whiskerRight_unit_iso_of_R_fully_faithful, Functor.IsDenseSubsite.isIso_ranCounit_app_of_isDenseSubsite, Mon.instIsIsoHomOfMapForget, Bicategory.conjugateEquiv_iso, Sheaf.isLocallySurjective_iff_isIso, ShortComplex.Exact.isIso_imageToKernel', AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.pullback_snd_isIso_of_range_subset, Limits.CatCospanTransform.isIso_right, IsPushout.isIso_inl_iso_of_epi, ObjectProperty.IsCodetecting.isIso_iff_of_epi, Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.isIso_post, instIsIsoF', Yoneda.isIso, Functor.Initial.limit_pre_isIso, Abelian.instIsIsoCoimageImageComparison, ShortComplex.Exact.isIso_toCycles, ShortComplex.instIsIsoRightHomologyMapOfEpiτ₁Ofτ₂OfMonoτ₃, WithInitial.isIso_of_to_star, TopCat.Presheaf.isIso_iff_stalkFunctor_map_iso, AlgebraicGeometry.isIso_fromTildeΓ_iff, IsIso.instMonoidalOppositeMop, mono_iff_isIso_snd, Functor.isLeftDerivedFunctor_iff_isIso_leftDerivedLift, Adjunction.instIsIsoMapAppCounitOfFaithfulOfFull, isIso_prod_iff, Limits.PushoutCocone.isIso_inr_of_epi_of_isColimit, Action.isIso_hom_mk, Limits.BinaryFan.isLimit_iff_isIso_snd, Cat.Hom.instIsIsoFunctorαCategoryToNatTransHomHom, Subfunctor.Subpresheaf.eq_top_iff_isIso, HomologicalComplex.isIso_homologyι, Sheaf.isConstant_iff_isIso_counit_app, MonoidalCategory.MonoidalRightAction.isIso_actionHomRight, DerivedCategory.isIso_Q_map_iff_quasiIso, DerivedCategory.isIso_Qh_map_iff, Limits.pullback.map_isIso, TopCat.Presheaf.stalkPushforward.stalkPushforward_iso_of_isInducing, Limits.CatCospanTransform.isIso_iff, CochainComplex.isIso_homologyπ₀, hoFunctor.isIso_prodComparison, Functor.isIso_lanAdjunction_counit_app_iff, Limits.Cones.cone_iso_of_hom_iso, Adjunction.isIso_counit_app_iff_mem_essImage, Abelian.isIso_factorThruCoimage, SmallObject.instIsIsoRightAppArrowιIteration, Limits.Types.isIso_colimitPointwiseProductToProductColimit, Pretriangulated.Triangle.isZero₁_iff_isIso₂, Functor.coreflective, LocalizerMorphism.isIso_iff_of_hasLeftResolutions, instIsIsoSSetProdComparisonCatCompNerveFunctorHoFunctorOf, Limits.isIso_limit_cone_parallelPair_of_self, nerveAdjunction.isIso_counit, isDetector_def, isIso_of_hom_comp_eq_id, Presheaf.instIsIsoFunctorLeftKanExtensionUnitOppositeTypeUliftYoneda, Limits.instIsIsoMapOfEpi, epi_iff_isIso_inr, Limits.pushout.map_isIso, GrothendieckTopology.isIso_toPlus_of_isSheaf, IsIso.id, Limits.Cocones.instIsIsoCoconeExtend, Functor.instIsIsoAppRanCounit_1, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓFreeOpensCarrierCarrierCommRingCat, Pretriangulated.isIso₁_of_isIso₂₃, Limits.IsLimit.isIso_π_app_of_isInitial, Limits.isIso_inl_of_epi, Adjunction.whiskerLeft_unit_iso_of_R_fully_faithful, Localization.LeftBousfield.W_iff_isIso_map, Profinite.isIso_asLimitCone_lift, HomologicalComplexUpToQuasiIso.isIso_Q_map_iff_mem_quasiIso, ShortComplex.Exact.isIso_fromOpcycles, AlgebraicGeometry.IsClosedImmersion.isIso_iff_ker_eq_bot, LocalizerMorphism.isIso_α_iff_of_isRightDerivabilityStructure, Limits.coequalizer.π_of_eq, IsPushout.isIso_inl_of_isIso, LocalizerMorphism.instIsIsoFunctorRightDerivedFunctorComparison, ComposableArrows.isIso_iff₁, instIsIsoPost, ShortComplex.isIso_iff, isIso_op_iff, MonoidalCategory.whiskerLeft_isIso, Limits.IsLimit.hom_isIso, AlgebraicGeometry.IsClosedImmersion.isIso_of_injective_of_isAffine, GrpObj.instIsIsoInv, Limits.isIso_limit_cocone_parallelPair_of_epi, Functor.mem_homologicalKernel_trW_iff, Limits.instIsIsoHomHomCone, AlgebraicGeometry.isIso_pushoutSection_of_isAffineOpen, Limits.cokernel.of_kernel_of_mono, SSet.Subcomplex.instIsIsoToRangeOfMono, Limits.isIso_ι_of_isTerminal, CartesianMonoidalCategory.isIso_prodComparison_of_preservesLimit_pair, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.instIsIsoInvApp, Reflective.instIsIsoAppUnitReflectorAdjunctionA, groupCohomology.isIso_δ_of_isZero, Monoidal.Reflective.instIsIsoMapTensorHomAppUnit, Arrow.isIso_right, Functor.OplaxMonoidal.instIsIsoδ, MonoOver.isIso_iff_isIso_left, instIsIsoFromLeftDerivedZero', ShortComplex.RightHomologyMapData.quasiIso_iff, MonoOver.instIsIsoLeftDiscretePUnitHomFullSubcategoryOverIsMono, ShortComplex.quasiIso_iff_isIso_liftCycles, FGModuleCat.instIsIsoCoimageImageComparison, WithTerminal.isIso_of_from_star, PreGaloisCategory.has_non_trivial_subobject_of_not_isConnected_of_not_initial, MonoidalCategory.MonoidalLeftAction.isIso_actionHomRight

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