Under π | CompOp | 272 mathmath: CommRingCat.tensorProd_map_right, Limits.Cone.toUnder_pt, StructuredArrow.instFullUnderToUnder, StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_left, Limits.PreservesColimitsOfSize.underPost, StructuredArrow.ofCommaSndEquivalenceFunctor_map_right, StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_right_right, IsGrothendieckAbelian.IsPresentable.injectivityβ.F_obj, Under.postComp_inv_app_right, StructuredArrow.ofDiagEquivalence.inverse_map_right, StructuredArrow.ofCommaSndEquivalence_functor, Under.forgetMapInitial_inv_app, Under.post_comp, WithInitial.isColimitEquiv_apply_desc_right, Under.equivalenceOfIsInitial_counitIso, WithInitial.coconeEquiv_functor_obj_pt, StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_right_left_as, Under.postCongr_inv_app_right, StructuredArrow.toUnder_obj_left, Under.mapIso_functor, IsGrothendieckAbelian.IsPresentable.injectivityβ.g_app, Under.instHasLimitsOfShape, Limits.pushoutCoconeEquivBinaryCofan_inverse_obj, Limits.pushoutCoconeEquivBinaryCofan_functor_obj, WithInitial.coconeEquiv_inverse_obj_pt_right, Limits.pushoutCoconeEquivBinaryCofan_unitIso, MorphismProperty.instIsClosedUnderIsomorphismsUnderUnderObjOfRespectsIso, CommRingCat.toAlgHom_comp, StructuredArrow.ofDiagEquivalence.functor_obj_right_right, Under.equivalenceOfIsInitial_functor, WithInitial.isColimitEquiv_symm_apply_desc, Limits.Cocone.underPost_ΞΉ_app, instHasColimitsOfShapeUnderOfWithInitial, Over.opEquivOpUnder_unitIso, Under.epi_of_epi_right, Under.liftCone_pt, WithInitial.liftFromUnderComp_inv_app, StructuredArrow.ofDiagEquivalence.inverse_obj_right, Under.forget_faithful, Under.mapCongr_inv_app, Under.pushoutIsLeftAdjoint, StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_left_as, MorphismProperty.ind_iff_ind_underMk, Under.mapFunctor_obj, instHasColimitsOfSizeUnder, Under.pushout_map, Under.lift_obj, WithInitial.coconeEquiv_inverse_obj_pt_hom, Limits.pushoutCoconeEquivBinaryCofan_inverse_map_hom, CommRingCat.Under.preservesFiniteLimits_of_flat, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right_assoc, StructuredArrow.ofCommaSndEquivalence_unitIso, Under.postAdjunctionRight_unit_app_right, StructuredArrow.ofCommaSndEquivalence_counitIso, Under.map_map_right, Over.opEquivOpUnder_inverse_obj, Limits.Cone.toStructuredArrowCompToUnderCompForget_hom_app, AlgHom.toUnder_comp, StructuredArrow.ofDiagEquivalence.inverse_obj_hom, Under.map_obj_right, Under.post_obj, StructuredArrow.ofDiagEquivalence.functor_obj_right_hom, commAlgCatEquivUnder_functor_obj, StructuredArrow.ofCommaSndEquivalenceInverse_map_right_left, Under.eqToHom_right, CommRingCat.Under.instPreservesFiniteLimitsUnderTensorProdOfFlatCarrier, Under.mapId_inv, Enriched.FunctorCategory.coneFunctorEnrichedHom_Ο_app, StructuredArrow.ofDiagEquivalence.functor_map_right_right, StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_left_as, Presheaf.functorEnrichedHomCoyonedaObjEquiv_naturality, WithInitial.coconeEquiv_counitIso_inv_app_hom, CommRingCat.Under.instPreservesLimitsOfShapeUnderWalkingParallelPairTensorProdOfFlatCarrier, MorphismProperty.under_eq_inverseImage, WithInitial.commaFromUnder_map_left, NatTrans.instIsClosedUnderColimitsOfShapeUnderFunctorCoequifiberedHomDiscretePUnitOfHasProductsOfShapeHom, Limits.Cone.toStructuredArrow_comp_toUnder_comp_forget, Under.costar_obj_left, Under.isoMk_inv_right, Under.mapPushoutAdj_unit_app, StructuredArrow.ofCommaSndEquivalenceFunctor_map_left, Under.instIsEquivalenceMapOfIsIso, WithInitial.coconeEquiv_functor_obj_ΞΉ_app_star, Over.opEquivOpUnder_inverse_map, Under.liftCocone_ΞΉ_app, Under.post_map, AlgEquiv.toUnder_trans, WithInitial.coconeEquiv_unitIso_hom_app_hom_right, Functor.essImage_underPost, Under.instFaithfulObjPost, Under.map_obj_hom, CommRingCat.Under.tensorProdEqualizer_ΞΉ, Under.instEssSurjObjPostOfFull, CommRingCat.Under.instPreservesFiniteProductsUnderPushout, CommRingCat.toAlgHom_id, Under.mono_iff_mono_right, WithInitial.liftFromUnder_obj_obj, StructuredArrow.isEquivalence_toUnder, StructuredArrow.ofStructuredArrowProjEquivalence.functor_map_right_right, Under.forgetCone_pt, StructuredArrow.ofCommaSndEquivalenceFunctor_obj_right, Under.postEquiv_counitIso, Under.postComp_hom_app_right, Limits.PreservesFiniteColimits.underPost, WithInitial.coconeEquiv_functor_map_hom, Under.isoMk_hom_right, StructuredArrow.ofDiagEquivalence.functor_obj_right_left_as, algebraEquivUnder_inverse, WithInitial.coconeEquiv_inverse_obj_pt_left_as, underToAlgebra_obj_A, Under.mapCongr_hom_app, AlgEquiv.toUnder_inv_right_apply, StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_hom, Limits.Cone.mapConeToUnder_inv_hom, StructuredArrow.toUnder_map_right, Under.instIsRightAdjointForget, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right_assoc, Under.mapFunctor_map, Under.liftCone_Ο_app, Under.instIsLeftAdjointCostar, IsGrothendieckAbelian.IsPresentable.injectivityβ.F_map, Under.forgetMapInitial_hom_app, Limits.pushoutCoconeEquivBinaryCofan_functor_map_hom, WithInitial.coconeEquiv_inverse_obj_ΞΉ_app_right, CommRingCat.monoidAlgebra_map, MorphismProperty.instFullUnderTopUnderForget, WithInitial.coconeEquiv_functor_obj_ΞΉ_app_of, Under.mapComp_hom, StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_hom, Under.opEquivOpOver_functor_obj, WithInitial.commaFromUnder_obj_hom_app, WithInitial.commaFromUnder_obj_right, Under.forget_map, commAlgCatEquivUnder_counitIso, StructuredArrow.instFaithfulUnderToUnder, isCardinalFiltered_under, Under.equivalenceOfIsInitial_unitIso, Under.isLeftAdjoint_post, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right, Over.opEquivOpUnder_counitIso, commAlgCatEquivUnder_inverse_obj_carrier, CommRingCat.Under.instPreservesLimitUnderDiscreteFunctorTensorProdOfFinite, Under.mapIso_inverse, Functor.toUnder_comp_forget, StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_right, AlgEquiv.toUnder_hom_right_apply, preservesFilteredColimits_coyoneda, StructuredArrow.ofStructuredArrowProjEquivalence.inverse_map_right_right, Enriched.FunctorCategory.functorEnrichedComp_app, commAlgCatEquivUnder_unitIso, CommRingCat.isFinitelyPresentable_under, Under.instIsEquivalenceObjPost, algebraEquivUnder_unitIso, underToAlgebra_obj_a, algebraToUnder_obj, WithInitial.commaFromUnder_map_right, StructuredArrow.ofCommaSndEquivalenceInverse_obj_hom, Enriched.FunctorCategory.functorEnrichedHom_obj, Under.postMap_app, Functor.toUnder_obj_right, Under.hom_right_inv_right, Under.mapId_hom, Under.postEquiv_inverse, StructuredArrow.toUnder_obj_hom, algebraEquivUnder_counitIso, Under.postCongr_hom_app_right, Enriched.FunctorCategory.instHasEnrichedHomUnderCompMapForget, MorphismProperty.Under.forget_comp_forget_map, StructuredArrow.ofCommaSndEquivalenceInverse_map_right_right, CommRingCat.tensorProdIsoPushout_app, Under.mapId_eq, Under.pushout_obj, WithInitial.commaFromUnder_obj_left, Limits.IsColimit.pushoutCoconeEquivBinaryCofanFunctor_desc_right, Under.instHasLimits, IsFiltered.under, commAlgCatEquivUnder_inverse_map, Under.hasColimit_of_hasColimit_liftFromUnder, Under.forget_obj, Under.liftCocone_pt, WithInitial.coconeEquiv_inverse_map_hom_right, CommRingCat.Under.instPreservesFiniteProductsUnderTensorProd, Under.mapForget_eq, underToAlgebra_map_f, Under.instFullObjPostOfFaithful, Under.final_forget, preservesColimit_coyoneda_of_finitePresentation, Functor.toUnder_map_right, Under.mono_of_mono_right, Under.mapPushoutAdj_counit_app, Under.mapComp_eq, WithInitial.liftFromUnderComp_hom_app, StructuredArrow.ofCommaSndEquivalenceFunctor_obj_left, StructuredArrow.ofDiagEquivalence.functor_obj_hom, CommRingCat.Under.equalizerFork_ΞΉ, WithInitial.coconeEquiv_counitIso_hom_app_hom, Limits.Cone.toUnder_Ο_app, Under.postAdjunctionLeft_counit_app, Under.inv_right_hom_right, WithInitial.liftFromUnder_map_app, Under.mapComp_inv, MorphismProperty.underObj_ind_eq_ind_underObj, commAlgCatEquivUnder_functor_map, StructuredArrow.ofDiagEquivalence.inverse_obj_left_as, Under.hom_right_inv_right_assoc, Under.locallySmall, CommRingCat.instIsLeftAdjointCommMonCatUnderMonoidAlgebra, CommRingCat.monoidAlgebra_obj, Limits.Cone.mapConeToUnder_hom_hom, Under.opEquivOpOver_inverse_obj, Under.costar_map_left, Under.equivalenceOfIsInitial_inverse_map, StructuredArrow.ofCommaSndEquivalence_inverse, Under.opEquivOpOver_counitIso, StructuredArrow.toUnder_map_left, WithInitial.liftFromUnder_obj_map, Enriched.FunctorCategory.functorHomEquiv_apply_app, Under.mkIdInitial_to_right, Under.mono_homMk, Under.equivalenceOfIsInitial_inverse_obj, Under.costar_obj_hom, StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_left_as, Limits.PreservesColimitsOfShape.underPost, Under.postAdjunctionRight_counit_app_right, Limits.pushoutCoconeEquivBinaryCofan_counitIso, isFinitelyPresentable, Over.opEquivOpUnder_functor_map, Under.postEquiv_functor, Under.lift_map, Under.hasLimit_of_hasLimit_comp_forget, Under.opEquivOpOver_unitIso, StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_hom, StructuredArrow.instEssSurjUnderToUnder, Under.inv_right_hom_right_assoc, Limits.Cone.toStructuredArrowCompToUnderCompForget_inv_app, IsGrothendieckAbelian.IsPresentable.injectivityβ.hf, Under.opEquivOpOver_functor_map, Under.epi_homMk, Under.postEquiv_unitIso, StructuredArrow.ofCommaSndEquivalenceInverse_obj_left_as, algebraToUnder_map, Limits.instPreservesFilteredColimitsOfSizeUnderForget, CommRingCat.Under.instPreservesLimitUnderWalkingParallelPairParallelPairTensorProdOfFlatCarrier, Under.id_right, algebraEquivUnder_functor, Under.homMk_comp, Under.postAdjunctionLeft_unit_app, StructuredArrow.ofDiagEquivalence.functor_obj_left_as, Enriched.FunctorCategory.functorEnrichedHom_map, StructuredArrow.toUnder_obj_right, CommRingCat.preservesFilteredColimits_coyoneda, Under.isRightAdjoint_post, WithInitial.coconeEquiv_unitIso_inv_app_hom_right, Under.opEquivOpOver_inverse_map, Under.preservesLimitsOfSize_map, Limits.Cocone.underPost_pt, CommRingCat.preservesColimit_coyoneda_of_finitePresentation, Under.forgetCone_Ο_app, StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_right_hom, IsGrothendieckAbelian.IsPresentable.injectivityβ.epi_f, StructuredArrow.ofCommaSndEquivalenceFunctor_obj_hom, Over.opEquivOpUnder_functor_obj, CommRingCat.Under.equalizer_comp, Under.forget_reflects_iso, CommRingCat.Under.equalizerFork'_ΞΉ, StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_hom, StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_right, Enriched.FunctorCategory.functorEnrichedId_app, Under.comp_right, MorphismProperty.instFaithfulUnderTopUnderForget, Under.faithful_pushout, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right
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instCategoryOver π | CompOp | 806 mathmath: TopCat.Presheaf.generateEquivalenceOpensLe_functor'_obj_obj, Over.associator_hom_left_snd_fst_assoc, GrothendieckTopology.overMapPullbackId_hom_app_val_app, ChosenPullbacksAlong.Over.whiskerLeft_left_fst, Over.prodLeftIsoPullback_hom_snd_assoc, Limits.IndizationClosedUnderFilteredColimitsAux.exists_nonempty_limit_obj_of_isColimit, Over.ΞΌ_pullback_left_snd', WithTerminal.coneEquiv_unitIso_hom_app_hom_left, Pseudofunctor.DescentData.subtypeCompatibleHomEquiv_toCompatible_presheafHomObjHomEquiv, CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_hom, Over.ConstructProducts.has_over_limit_discrete_of_widePullback_limit, Subobject.factors_iff, ChosenPullbacksAlong.Over.associator_hom_left_snd_fst_assoc, Over.faithful_pullback, Over.forget_faithful, Over.instHasTerminal, AlgebraicGeometry.Scheme.Cover.pullbackCoverOver_X, Over.ConstructProducts.conesEquivInverseObj_pt, MorphismProperty.over_eq_inverseImage, Over.iteratedSliceForwardNaturalityIso_hom_app, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_mapβ, CostructuredArrow.toOver_obj_left, MonoOver.mk_coe, ChosenPullbacksAlong.Over.tensorHom_left_fst, AlgebraicGeometry.isCommMonObj_of_isProper_of_geometricallyIntegral, OverPresheafAux.costructuredArrowPresheafToOver_map, Over.forgetCocone_pt, AlgebraicGeometry.opensCone_pt, ChosenPullbacksAlong.cartesianMonoidalCategoryFst_pullback_map, MonoOver.congr_unitIso, MorphismProperty.HasFactorization.over, instGuitartExactOverObjOverPostOfHasBinaryProductOfPreservesLimitDiscreteWalkingPairPair, instHasLimitsOfSizeOver, OverPresheafAux.unitAux_hom, Over.iteratedSliceBackward_map, CostructuredArrow.ofDiagEquivalence.functor_map_left_left, IsGrothendieckAbelian.IsPresentable.injectivityβ.F_obj, MonoOver.mapIso_functor, Over.associator_inv_left_snd, ExponentiableMorphism.homEquiv_symm_apply_eq, Limits.Cocone.toOver_ΞΉ_app, Over.pullback_obj_left, AlgebraicGeometry.Scheme.restrictFunctorΞ_inv_app, Over.inv_left_hom_left_assoc, Over.instIsLeftAdjointForget, AlgebraicGeometry.Scheme.overGrothendieckTopology_eq_toGrothendieck_overPretopology, TopCat.Presheaf.generateEquivalenceOpensLe_unitIso, MonoOver.mk_obj, Over.mapIso_inverse, MonoOver.isIso_left_iff_subobjectMk_eq, GrothendieckTopology.overMapPullback_comp_id, Sieve.overEquiv_pullback, Over.rightUnitor_inv_left_fst_assoc, OverPresheafAux.restrictedYoneda_map, GrothendieckTopology.overMapPullbackId_inv_app_val_app, toOver_obj_hom, MonoOver.hasColimitsOfSize_of_hasStrongEpiMonoFactorisations, Sieve.ofArrows_category', Over.comp_left_assoc, GrothendieckTopology.instIsContinuousOverStarOver, ExponentiableMorphism.id_pushforward, Iso.asOver_hom, MonoOver.instIsRightAdjointOverForget, Over.hom_left_inv_left, Over.instIsEquivalenceObjPost, Limits.PreservesLimitsOfShape.overPost, Over.monObjMkPullbackSnd_mul, Over.whiskerLeft_left, Over.forgetMapTerminal_hom_app, OverPresheafAux.restrictedYoneda_obj, Over.equivalenceOfIsTerminal_counitIso, Presheaf.isSheaf_iff_isLimit_coverage, MonoOver.isIso_iff_subobjectMk_eq, Over.epi_iff_epi_left, Over.grpObjMkPullbackSnd_one, Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp, AlgebraicGeometry.Scheme.Cover.pullbackCoverOver'_X, CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_left_hom, WithTerminal.coneEquiv_inverse_obj_Ο_app_left, Over.grpObjMkPullbackSnd_mul, CostructuredArrow.toOver_obj_right, AlgebraicGeometry.Scheme.locallyCoverDense_of_le, CostructuredArrow.ofDiagEquivalence.inverse_obj_left, ChosenPullbacksAlong.unit_pullbackComp_hom_assoc, Over.hasLimit_of_hasLimit_liftFromOver, OverClass.asOverHom_comp_assoc, MonoOver.mapIso_unitIso, toOver_obj_left, IsGrothendieckAbelian.IsPresentable.surjectivity.F_map, ChosenPullbacksAlong.iso_mapPullbackAdj_unit_app, toOverPullbackIsoToOver_inv_app_left, Over.toUnit_left, GrothendieckTopology.over_map_coverPreserving, coalgebraEquivOver_functor, ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd_assoc, Limits.Cocone.toCostructuredArrow_comp_toOver_comp_forget, Over.braiding_inv_left, Over.mapId_eq, CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompCoyoneda, Over.opEquivOpUnder_unitIso, Over.prodLeftIsoPullback_inv_snd, Over.iteratedSliceForwardIsoPost_inv_app, toOverUnit_map_left, instIsContinuousOverLeftDiscretePUnitIteratedSliceForwardOver, MonoOver.mapIso_counitIso, ExponentiableMorphism.comp_pushforward, Over.leftUnitor_hom_left, Over.isCommMonObj_mk_pullbackSnd, Over.tensorObj_ext_iff, CostructuredArrow.toOver_map_right, HomotopicalAlgebra.instIsStableUnderRetractsOverFibrations, Over.iteratedSliceForward_forget, Types.monoOverEquivalenceSet_inverse_map, toOverIsoToOverUnit_inv_app_left, Over.ConstructProducts.conesEquivCounitIso_inv_app_hom_left, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_obj_obj_right_as, MorphismProperty.baseChange_map, Over.postAdjunctionRight_counit_app, Over.conePost_obj_Ο_app, MonoOver.mkArrowIso_hom_hom_left, NatTrans.instIsClosedUnderLimitsOfShapeOverFunctorEquifiberedHomDiscretePUnitOfHasCoproductsOfShapeHom, CostructuredArrow.toOver_obj_hom, Sieve.overEquiv_le_overEquiv_iff, CostructuredArrow.instFullOverToOver, MonoOver.map_obj_left, ChosenPullbacksAlong.snd'_left, ChosenPullbacksAlong.Over.tensorObj_ext_iff, CostructuredArrow.ofDiagEquivalence.functor_obj_hom, Over.rightUnitor_inv_left_fst, Over.ConstructProducts.conesEquiv_unitIso, WithTerminal.commaFromOver_map_left, ChosenPullbacksAlong.Over.tensorHom_left_snd_assoc, ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_unit_app, MonoOver.isIso_hom_left_iff_subobjectMk_eq, Over.mapCongr_inv_app_left, CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_right_as, Limits.PreservesFiniteLimits.overPost, Sieve.ofArrows_category, Over.mapCongr_hom_app_left, ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd, equivToOverUnit_unitIso, Over.postCongr_inv_app_left, ChosenPullbacksAlong.isoInv_pullback_obj_left, CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_hom, Over.mapComp_hom_app_left, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_obj_obj_hom, essentiallySmall_monoOver, Over.whiskerRight_left_fst, Limits.colimit.toOver_ΞΉ_app, Over.postAdjunctionLeft_unit_app_left, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_comp_val_app, CostructuredArrow.costructuredArrowToOverEquivalence.functor_map, GrothendieckTopology.pseudofunctorOver_mapComp_inv_toNatTrans_app_val_app, MonoOver.pullback_obj_arrow, Over.preservesTerminalIso_pullback, WithTerminal.commaFromOver_obj_right, Over.prodLeftIsoPullback_inv_fst, Presheaf.isLimit_iff_isSheafFor_presieve, WithTerminal.coneEquiv_functor_obj_Ο_app_star, CostructuredArrow.ofDiagEquivalence.functor_obj_left_hom, WithTerminal.coneEquiv_counitIso_inv_app_hom, Over.opEquivOpUnder_inverse_obj, MorphismProperty.instFaithfulOverTopOverForget, CostructuredArrow.instFaithfulOverToOver, AlgebraicGeometry.Scheme.kerAdjunction_unit_app, Over.prodLeftIsoPullback_inv_snd_assoc, Over.rightUnitor_inv_left_snd, ChosenPullbacksAlong.Over.tensorObj_hom, Over.coprod_obj, AlgebraicGeometry.instIsClosedImmersionLeftSchemeDiscretePUnitOneOverSpecOf, Over.post_map, GrothendieckTopology.instIsCocontinuousOverForgetOver, regularTopology.equalizerConditionMap_iff_nonempty_isLimit, Pseudofunctor.presheafHom_obj, instInitialCostructuredArrowOverToOver, Over.mapPullbackAdj_counit_app, Over.iteratedSliceBackward_forget, Over.postCongr_hom_app_left, toOverUnit_obj_left, instInitiallySmallOverOfLocallySmall, Limits.pullbackConeEquivBinaryFan_functor_map_hom, ChosenPullbacksAlong.Over.tensorObj_left, Over.iteratedSliceBackward_forget_forget, Over.instHasColimitsOfShape, presheafHom_obj, ChosenPullbacksAlong.Over.associator_hom_left_fst, IsCofiltered.over, Over.prodLeftIsoPullback_hom_snd, Over.locallySmall, Limits.pullbackConeEquivBinaryFan_counitIso, ChosenPullbacksAlong.isoInv_pullback_map_left, CostructuredArrow.ofCommaFstEquivalence_inverse, GrothendieckTopology.coverPreserving_over_star, Over.whiskerRight_left_snd_assoc, ChosenPullbacksAlong.Over.snd_eq_snd', Limits.IsLimit.pullbackConeEquivBinaryFanFunctor_lift_left, Over.associator_inv_left_fst_fst_assoc, Sieve.overEquiv_symm_iff, AlgebraicGeometry.Scheme.isCommMonObj_asOver_pullback, GrothendieckTopology.overEquiv_symm_mem_over, Sieve.functorPushforward_over_map, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_val_obj, Over.epi_of_epi_left, CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_hom, Over.associator_hom_left_fst, GrothendieckTopology.over_forget_compatiblePreserving, Limits.Cocone.toCostructuredArrowCompToOverCompForget_inv_app, Subfunctor.equivalenceMonoOver_inverse_map, AlgebraicGeometry.Scheme.isMonHom_fst_id_right, Over.forgetAdjStar_counit_app, ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd, OverClass.asOverHom_inv, ChosenPullbacksAlong.Over.tensorUnit_hom, Over.prodLeftIsoPullback_hom_fst_assoc, Over.map_map_left, ChosenPullbacksAlong.Over.whiskerLeft_left_snd_assoc, CostructuredArrow.instEssSurjOverToOver, ExponentiableMorphism.pushforwardId_hom_counit_assoc, CostructuredArrow.ofDiagEquivalence.functor_obj_left_left, ChosenPullbacksAlong.Over.associator_hom_left_snd_fst, MonoOver.image_map, GrothendieckTopology.mem_over_iff, Over.tensorUnit_hom, Over.opEquivOpUnder_inverse_map, Subfunctor.equivalenceMonoOver_functor_map, CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_map_left_left, presheafHom_map_app, AlgebraicGeometry.instFaithfulOverSchemePullbackOfSurjectiveOfFlatOfQuasiCompact, Limits.instPreservesCofilteredLimitsOfSizeOverForget, Over.leftUnitor_inv_left_fst, ChosenPullbacksAlong.isoInv_mapPullbackAdj_unit_app_left, Over.inv_left_hom_left, Over.starPullbackIsoStar_hom_app_left, Over.equivalenceOfIsTerminal_inverse_map, Over.postEquiv_inverse, AlgebraicGeometry.opensDiagram_map, ChosenPullbacksAlong.Over.whiskerRight_left, HomotopicalAlgebra.cofibrations_over_iff, CostructuredArrow.ofDiagEquivalence.inverse_obj_hom, WithTerminal.coneEquiv_functor_obj_Ο_app_of, Over.forgetMapTerminal_inv_app, HomotopicalAlgebra.trivialFibrations_over_eq, ChosenPullbacksAlong.unit_pullbackId_hom_app, Over.instIsRightAdjointStar, Subobject.inf_eq_map_pullback', Over.equivalenceOfIsTerminal_functor, Over.preservesColimitsOfSize_map, OverClass.asOverHom_id, Presheaf.isSeparated_iff_subsingleton, Over.isoMk_inv_left, Over.conePostIso_hom_app_hom, Over.eqToHom_left, Sieve.overEquiv_top, Over.mapComp_eq, Over.tensorHom_left_snd_assoc, ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd_assoc, MorphismProperty.instIsClosedUnderIsomorphismsOverOverObjOfRespectsIso, Over.mono_homMk, ExponentiableMorphism.ev_coev, monoOver_terminal_to_subterminals_comp, HomotopicalAlgebra.instIsStableUnderRetractsOverCofibrations, Over.leftUnitor_inv_left_snd, ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst_assoc, AlgebraicGeometry.Scheme.kerAdjunction_counit_app, AlgebraicGeometry.opensDiagramΞΉ_app, Over.prodComparisonIso_pullback_inv_left_snd', GrothendieckTopology.overMapPullback_assoc_assoc, CostructuredArrow.ofCommaFstEquivalenceInverse_obj_right_as, Over.preservesLimitsOfShape_forget_of_isConnected, MonoOver.image_obj, TopologicalSpace.Opens.coe_overEquivalence_functor_obj, OverClass.instIsIsoOverAsOverHom, Over.ΞΌ_pullback_left_fst_snd', CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_left, Over.comp_left, ChosenPullbacksAlong.Over.tensorUnit_left, Over.mapPullbackAdj_unit_app, MorphismProperty.Over.forget_comp_forget_map, Over.mapId_inv_app_left, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_hom_app, ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst, Sieve.overEquiv_symm_pullback, Subfunctor.equivalenceMonoOver_inverse_obj, Over.leftUnitor_inv_left_snd_assoc, TopCat.Presheaf.whiskerIsoMapGenerateCocone_inv_hom, Over.ConstructProducts.conesEquivFunctor_map_hom, ChosenPullbacksAlong.iso_pullback_obj, WithTerminal.coneEquiv_inverse_obj_pt_left, Presieve.functorPushforward_overForget, Over.pullbackIsRightAdjoint, Over.conePost_map_hom, AlgebraicGeometry.Scheme.mem_overGrothendieckTopology, Over.over_hasTerminal, MonoOver.bot_left, Presieve.ofArrows_category, Over.lift_obj, TopologicalSpace.Opens.overEquivalence_unitIso_hom_app_left, AlgebraicGeometry.instIsAffineHomMapOverSchemeOpensDiagram, MonoOver.map_obj_arrow, Limits.pullbackConeEquivBinaryFan_inverse_obj, ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_unit_app, Limits.pullbackConeEquivBinaryFan_functor_obj, Over.map_obj_hom, Over.initial_forget, Over.associator_hom_left_snd_fst, CostructuredArrow.toOver_map_left, Over.postComp_inv_app_left, HomotopicalAlgebra.trivialCofibrations_over_eq, Over.toOverSectionsAdj_unit_app, subterminalsEquivMonoOverTerminal_inverse_map, Subobject.lower_comm, Functor.toOver_obj_left, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_str_id_val_app, Over.post_comp, Over.equivalenceOfIsTerminal_inverse_obj, Over.rightUnitor_inv_left_snd_assoc, Over.toOverSectionsAdj_counit_app, ChosenPullbacksAlong.Over.whiskerRight_left_snd, MonoOver.w, MonoOver.bot_arrow_eq_zero, CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompYoneda, forgetAdjToOver_unit_app, Over.iteratedSliceEquivOverMapIso_inv_app_left_left, MonoOver.hasFiniteLimits, Over.iteratedSliceEquivOverMapIso_hom_app_left_left, CostructuredArrow.costructuredArrowToOverEquivalence.functor_obj, WithTerminal.isLimitEquiv_symm_apply_lift, regularTopology.parallelPair_pullback_initial, WithTerminal.liftFromOver_obj_obj, overToCoalgebra_map_f, Over.isRightAdjoint_post, Pseudofunctor.isStackFor_iff, CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_left_right_as, Subfunctor.equivalenceMonoOver_functor_obj, Limits.Cocone.toOver_pt, Pseudofunctor.isPrestackFor_iff_isSheafFor, ChosenPullbacksAlong.Over.whiskerRight_left_snd_assoc, ChosenPullbacksAlong.Over.whiskerRight_left_fst_assoc, AlgebraicGeometry.Scheme.restrictFunctorΞ_hom_app, Pseudofunctor.bijective_toDescentData_map_iff, Over.ConstructProducts.conesEquivUnitIso_inv_app_hom, Over.pullback_map_left, instIsContinuousOverLeftDiscretePUnitIteratedSliceBackwardOver, IsGrothendieckAbelian.IsPresentable.injectivityβ.F_map, isEventuallyConstant_of_isArtinianObject, Over.prodComparisonIso_pullback_inv_left_fst_fst, Pseudofunctor.presheafHom_map, WithTerminal.coneEquiv_inverse_obj_pt_hom, Over.postEquiv_counitIso, ChosenPullbacksAlong.pullbackId_hom_counit, ExponentiableMorphism.ev_def, Over.ConstructProducts.conesEquivCounitIso_hom_app_hom_left, Over.sections_obj, AlgebraicGeometry.opensDiagram_obj, Over.star_obj_left, AlgebraicGeometry.Scheme.instFullOppositeIdealSheafDataOverSubschemeFunctor, WithTerminal.liftFromOverComp_hom_app, equivToOverUnit_counitIso, Over.iteratedSliceEquiv_functor, AlgebraicGeometry.opensCone_Ο_app, Over.tensorHom_left, CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_right_as, toOverIteratedSliceForwardIsoPullback_hom_app_left, MonoOver.mk'_coe', ExponentiableMorphism.ev_coev_assoc, CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_left_hom, Presheaf.isSheaf_iff_isLimit, Under.opEquivOpOver_functor_obj, Over.ConstructProducts.conesEquiv_counitIso, MonoOver.mono, Over.associator_inv_left_fst_snd, MonoOver.forget_obj_left, Subobject.instIsEquivalenceMonoOverRepresentative, Over.forget_obj, Over.closedUnderLimitsOfShape_pullback, toOverPullbackIsoToOver_hom_app_left, Over.star_obj_hom, Over.forgetPreservesConnectedLimits, coalgebraToOver_obj, Over.associator_hom_left_snd_snd_assoc, Limits.Cone.overPost_pt, ExponentiableMorphism.pushforwardComp_hom_counit_assoc, ExponentiableMorphism.coev_def, Over.liftCone_Ο_app, CostructuredArrow.ofCommaFstEquivalence_functor, TopologicalSpace.Opens.overEquivalence_counitIso_inv_app, Over.instIsEquivalenceMapOfIsIso, ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst, TopCat.Presheaf.generateEquivalenceOpensLe_functor, Over.ΞΌ_pullback_left_fst_fst', ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_pullback_obj, CostructuredArrow.ofCommaFstEquivalenceFunctor_map_right, Types.monoOverEquivalenceSet_functor_map, Over.ΞΌ_pullback_left_fst_snd, Over.whiskerRight_left, Over.monObjMkPullbackSnd_one, TopologicalSpace.Opens.overEquivalence_unitIso_inv_app_left, AlgebraicGeometry.Scheme.IdealSheafData.subschemeFunctor_obj, ExponentiableMorphism.ev_naturality_assoc, CostructuredArrow.ofDiagEquivalence.functor_obj_right_as, Over.opEquivOpUnder_counitIso, Over.hasFiniteLimits, AlgebraicGeometry.instIsOpenImmersionMapSchemeCompOverOverTopMorphismPropertyForgetForget, GrothendieckTopology.overMapPullbackCongr_eq_eqToIso, Over.hasColimit_of_hasColimit_comp_forget, ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd, CostructuredArrow.ofCommaFstEquivalenceInverse_map_left_left, toOverIsoToOverUnit_hom_app_left, ChosenPullbacksAlong.cartesianMonoidalCategorySnd_pullback_map, TopCat.Presheaf.generateEquivalenceOpensLe_counitIso, SheafOfModules.instIsLeftAdjointOverOverRingCatPushforwardIdSheafOver, Sieve.yonedaFamily_fromCocone_compatible, subterminalsEquivMonoOverTerminal_inverse_obj_obj, ChosenPullbacksAlong.Over.whiskerLeft_left_fst_assoc, AlgebraicGeometry.Scheme.monObjAsOverPullback_mul, coalgebraEquivOver_counitIso, Over.closedUnderLimitsOfShape_discrete_empty, Types.monoOverEquivalenceSet_functor_obj, MonoOver.hasLimitsOfShape, AlgebraicGeometry.Scheme.kerFunctor_map, ChosenPullbacksAlong.pullbackId_hom_counit_assoc, MonoOver.congr_functor, Pseudofunctor.IsStack.essSurj_of_sieve, Over.associator_inv_left_fst_fst, Presieve.isSheafFor_over_map_op_comp_ofArrows_iff, Presieve.isSheafFor_over_map_op_comp_iff, CostructuredArrow.ofDiagEquivalence.inverse_obj_right_as, MonoOver.isIso_iff_isIso_hom_left, instHasLimitsOfShapeOverOfWithTerminal, Over.snd_left, CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_map_left_left, ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_snd, MonoOver.congr_inverse, ChosenPullbacksAlong.Over.tensorHom_left_fst_assoc, instIsCocontinuousOverLeftDiscretePUnitIteratedSliceBackwardOver, Over.tensorHom_left_fst, Sieve.overEquiv_symm_generate, Over.whiskerRight_left_snd, AlgebraicGeometry.Scheme.Cover.pullbackCoverOver_f, Over.conePostIso_inv_app_hom, ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_mapPullbackAdj_unit_app, ChosenPullbacksAlong.pullbackComp_hom_counit, TopCat.Presheaf.whiskerIsoMapGenerateCocone_hom_hom, ChosenPullbacksAlong.Over.associator_inv_left_fst_snd_assoc, ChosenPullbacksAlong.Over.associator_inv_left_fst_snd, WithTerminal.commaFromOver_obj_hom_app, AlgebraicGeometry.Scheme.Cover.toPresieveOver_le_arrows_iff, Over.iteratedSliceEquiv_unitIso, Classifier.SubobjectRepresentableBy.iso_inv_left_Ο_assoc, Over.isoMk_hom_left, HomotopicalAlgebra.fibrations_over_def, ChosenPullbacksAlong.Over.whiskerRight_left_fst, Functor.toOver_map_left, Over.star_map_left, Over.tensorHom_left_fst_assoc, ChosenPullbacksAlong.Over.associator_inv_left_snd_assoc, forgetAdjToOver.homEquiv_symm, AlgebraicGeometry.Scheme.Cover.overEquiv_generate_toPresieveOver_eq_ofArrows, CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_hom, Over.prodLeftIsoPullback_inv_fst_assoc, ChosenPullbacksAlong.Over.rightUnitor_hom_left, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map_val_app, HomotopicalAlgebra.cofibrations_over_def, Subobject.lowerEquivalence_counitIso, Pseudofunctor.IsPrestack.isSheaf, subterminalsEquivMonoOverTerminal_functor_map, Over.Ξ·_pullback_left, GrothendieckTopology.overMapPullback_comp_id_assoc, Pseudofunctor.presheafHomObjHomEquiv_apply, ExponentiableMorphism.coev_ev_assoc, Over.postAdjunctionRight_unit_app, Over.conePost_obj_pt, Over.id_left, ChosenPullbacksAlong.Over.leftUnitor_hom_left, ChosenPullbacksAlong.cartesianMonoidalCategoryFst_pullback_obj, Over.postComp_hom_app_left, HasLiftingProperty.over, IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver_map, Over.instHasFiniteColimits, Over.whiskerLeft_left_fst, CostructuredArrow.ofCommaFstEquivalence_counitIso, ChosenPullbacksAlong.cartesianMonoidalCategoryFst_mapPullbackAdj_counit_app, MonoOver.inf_map_app, MonoOver.isThin, CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_left, ChosenPullbacksAlong.isoInv_mapPullbackAdj_counit_app_left, Over.post_obj, Over.ConstructProducts.conesEquiv_functor, MonoOver.mkArrowIso_inv_hom_left, Over.epi_homMk, Limits.Cocone.toCostructuredArrowCompToOverCompForget_hom_app, MorphismProperty.Over.instPreservesFiniteLimitsTopOverForget, Pseudofunctor.isPrestackFor_iff, CostructuredArrow.ofCommaFstEquivalenceFunctor_map_left, ChosenPullbacksAlong.Over.lift_left, Over.mapId_hom_app_left, Limits.PreservesLimitsOfSize.overPost, Presieve.map_functorPullback_overForget, WithTerminal.commaFromOver_map_right, MonoOver.w_assoc, Over.forget_reflects_iso, Over.isPullback_of_binaryFan_isLimit, Pseudofunctor.IsStackFor.isEquivalence, Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp_assoc, Over.ConstructProducts.over_products_of_widePullbacks, MorphismProperty.instFullOverTopOverForget, CostructuredArrow.ofCommaFstEquivalenceFunctor_obj_right, Over.whiskerLeft_left_fst_assoc, MonoOver.pullback_obj_left, CostructuredArrow.ofCostructuredArrowProjEquivalence.functor_obj_left_left, AlgebraicGeometry.instIsOpenImmersionAppOverSchemeOpensDiagramΞΉ, Over.instFaithfulObjPost, Subobject.lowerEquivalence_unitIso, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_obj_val_map, Over.coprodObj_obj, GrothendieckTopology.overMapPullbackComp_inv_app_val_app, AlgebraicGeometry.isClosedImmersion_equalizer_ΞΉ_left, Iso.asOver_inv, ChosenPullbacksAlong.Over.associator_inv_left_fst_fst, ChosenPullbacksAlong.cartesianMonoidalCategorySnd_pullback_obj, CostructuredArrow.ofDiagEquivalence.functor_obj_left_right_as, Subfunctor.equivalenceMonoOver_unitIso, Over.prodComparisonIso_pullback_Spec_inv_left_fst_fst', AlgebraicGeometry.Scheme.instLocallyCoverDenseOverTopMorphismPropertyOverForgetOverGrothendieckTopology, MonoOver.subobjectMk_le_mk_of_hom, Over.ConstructProducts.over_binaryProduct_of_pullback, Over.whiskerLeft_left_snd_assoc, ChosenPullbacksAlong.unit_pullbackId_hom, Over.equivalenceOfIsTerminal_unitIso, TopologicalSpace.Opens.coe_overEquivalence_inverse_obj_left, Over.iteratedSliceEquiv_counitIso, HomotopicalAlgebra.instHasFactorizationOverTrivialCofibrationsFibrations, Over.leftUnitor_inv_left_fst_assoc, ChosenPullbacksAlong.Over.whiskerLeft_left, Sieve.forallYonedaIsSheaf_iff_colimit, WithTerminal.liftFromOver_obj_map, equivToOverUnit_inverse, Over.liftCocone_ΞΉ_app, Over.instHasFiniteCoproducts, HomotopicalAlgebra.instHasTwoOutOfThreePropertyOverWeakEquivalences, ExponentiableMorphism.coev_naturality_assoc, Limits.Cocone.mapCoconeToOver_inv_hom, ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_mapPullbackAdj_counit_app, WithTerminal.isLimitEquiv_apply_lift_left, subterminalsEquivMonoOverTerminal_unitIso, overToCoalgebra_obj_A, Over.postEquiv_unitIso, coalgebraToOver_map, ExponentiableMorphism.pushforwardComp_hom_counit, Pseudofunctor.IsStackFor.essSurj, GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_obj_Ξ±, Over.associator_inv_left_fst_snd_assoc, ChosenPullbacksAlong.cartesianMonoidalCategorySnd_mapPullbackAdj_counit_app, MonoOver.forget_obj_hom, Classifier.SubobjectRepresentableBy.iso_inv_left_comp, Over.rightUnitor_hom_left, Functor.over_forget_locallyCoverDense, Over.instHasPullbacks, Over.ConstructProducts.conesEquivFunctor_obj_pt, toOver_map_left, Over.sections_map, ChosenPullbacksAlong.fst'_left, CostructuredArrow.ofCommaFstEquivalenceInverse_obj_left_right, MonoOver.commSqOfHasStrongEpiMonoFactorisation, Over.ConstructProducts.over_finiteProducts_of_finiteWidePullbacks, ExponentiableMorphism.coev_naturality, Over.ΞΌ_pullback_left_snd, Over.iteratedSliceBackward_obj, subterminalsEquivMonoOverTerminal_counitIso, CostructuredArrow.ofDiagEquivalence.inverse_map_left, ChosenPullbacksAlong.Over.toUnit_left, Over.mapFunctor_obj, WithTerminal.coneEquiv_unitIso_inv_app_hom_left, Classifier.SubobjectRepresentableBy.iso_inv_left_Ο, Over.map_obj_left, AlgebraicGeometry.instIsLocallyDirectedCompSchemeOverOverTopMorphismPropertyForgetForgetForget, Types.monoOverEquivalenceSet_inverse_obj, ExponentiableMorphism.unit_pushforwardId_hom, Sieve.overEquiv_symm_top, MonoOver.hasLimit, PresheafHom.IsSheafFor.app_cond, coalgebraEquivOver_inverse, Over.instFullObjPostOfFaithful, Over.instEssSurjObjPostOfFull, Over.ConstructProducts.conesEquivUnitIso_hom_app_hom, Over.braiding_hom_left, MonoOver.instMonoHomDiscretePUnitObjOverForget, ChosenPullbacksAlong.Over.associator_inv_left_snd, ChosenPullbacksAlong.isoInv_pullback_obj_hom, ChosenPullbacksAlong.iso_mapPullbackAdj_counit_app, GrothendieckTopology.overMapPullbackComp_hom_app_val_app, IsGrothendieckAbelian.IsPresentable.surjectivity.F_obj, ChosenPullbacksAlong.Over.whiskerLeft_left_snd, ChosenPullbacksAlong.Over.associator_hom_left_snd_snd, overToCoalgebra_obj_a, ChosenPullbacksAlong.isoInv_pullback_obj_right_as, FunctorToTypes.mem_fromOverSubfunctor_iff, Over.ΞΌ_pullback_left_fst_fst, Over.starPullbackIsoStar_inv_app_left, GrothendieckTopology.instIsContinuousOverForgetOver, Over.iteratedSliceForward_map, GrothendieckTopology.overMapPullback_id_comp_assoc, AlgebraicGeometry.Scheme.instFullEtaleOverForget, MonoOver.inf_obj, AlgebraicGeometry.Scheme.Cover.pullbackCoverOver'_f, MonoOver.top_left, Over.tensorUnit_left, toOverIteratedSliceForwardIsoPullback_inv_app_left, Over.hom_left_inv_left_assoc, MorphismProperty.faithful_overPullback_of_isomorphisms_descendAlong, ChosenPullbacksAlong.iso_pullback_map, Under.opEquivOpOver_inverse_obj, PresheafHom.IsSheafFor.exists_app, CostructuredArrow.overEquivPresheafCostructuredArrow_functor_map_toOverCompCoyoneda, Over.ConstructProducts.conesEquivInverse_obj, GrothendieckTopology.pseudofunctorOver_mapComp_hom_toNatTrans_app_val_app, OverClass.asOverHom_comp, Types.monoOverEquivalenceSet_unitIso, CostructuredArrow.ofCommaFstEquivalence_unitIso, CostructuredArrow.costructuredArrowToOverEquivalence.inverse_obj, Over.iteratedSliceEquiv_inverse, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_obj_obj_left, ExponentiableMorphism.unit_pushforwardId_hom_assoc, AlgebraicGeometry.Scheme.kerFunctor_obj, ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst_assoc, ExponentiableMorphism.ev_naturality, IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver_obj, Over.forgetCocone_ΞΉ_app, WithTerminal.liftFromOverComp_inv_app, coalgebraEquivOver_unitIso, Over.whiskerRight_left_fst_assoc, Over.tensorHom_left_snd, Limits.Cone.overPost_Ο_app, Under.opEquivOpOver_counitIso, equivToOverUnit_functor, Over.forget_map, GrothendieckTopology.overMapPullbackCongr_hom_app_val_app, Subobject.representative_coe, MonoOver.full_map, CostructuredArrow.isEquivalence_toOver, CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_left_right_as, WithTerminal.liftFromOver_map_app, ChosenPullbacksAlong.unit_pullbackComp_hom, Sieve.overEquiv_generate, WithTerminal.coneEquiv_inverse_map_hom_left, Subobject.inf_eq_map_pullback, Over.postMap_app, GrothendieckTopology.instIsContinuousOverMapOver, Over.ConstructProducts.conesEquivInverseObj_Ο_app, ExponentiableMorphism.unit_pushforwardComp_hom, TopologicalSpace.Opens.overEquivalence_inverse_obj_right_as, AlgebraicGeometry.instIsQuasicoherentOpensCarrierCarrierCommRingCatSpecTilde, MonoOver.mapIso_inverse, Presheaf.isLimit_iff_isSheafFor, Over.instHasEqualizers, ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_fst_assoc, Over.lift_left, AlgebraicGeometry.Scheme.restrictFunctor_obj_left, MonoOver.congr_counitIso, Over.opEquivOpUnder_functor_map, AlgebraicGeometry.instPreservesColimitOverSchemeTopMorphismPropertyOverForget, PresheafHom.isAmalgamation_iff, Subobject.lowerEquivalence_inverse, Subobject.lowerEquivalence_functor, OverPresheafAux.costructuredArrowPresheafToOver_obj, GrothendieckTopology.over_map_compatiblePreserving, AlgebraicGeometry.instMonoObjWalkingSpanCompOverSchemeTopMorphismPropertySpanOverForgetForgetForgetNoneWalkingPairSomeMapInitOfIsOpenImmersionLeftDiscretePUnit, Over.mapIso_functor, AlgebraicGeometry.Scheme.monObjAsOverPullback_one, ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit_pullback_map, Limits.IndizationClosedUnderFilteredColimitsAux.exists_nonempty_limit_obj_of_colimit, AlgebraicGeometry.Scheme.restrictFunctor_map_left, ChosenPullbacksAlong.pullbackIsoOverPullback_hom_app_comp_fst, CostructuredArrow.overEquivPresheafCostructuredArrow_inverse_map_toOverCompYoneda, TopCat.Presheaf.generateEquivalenceOpensLe_functor'_map, Limits.Cocone.mapCoconeToOver_hom_hom, HomotopicalAlgebra.weakEquivalences_over_iff, Under.opEquivOpOver_unitIso, Over.ConstructProducts.over_product_of_widePullback, sheafHomSectionsEquiv_symm_apply_coe_apply, Over.mkIdTerminal_from_left, ChosenPullbacksAlong.Over.fst_eq_fst', WithTerminal.coneEquiv_functor_obj_pt, Under.opEquivOpOver_functor_map, Over.ConstructProducts.conesEquiv_inverse, HomotopicalAlgebra.instHasFactorizationOverCofibrationsTrivialFibrations, Functor.essImage_overPost, WithTerminal.commaFromOver_obj_left, TopologicalSpace.Opens.overEquivalence_counitIso_hom_app, Over.fst_left, Over.prodLeftIsoPullback_hom_fst, GrothendieckTopology.overMapPullback_assoc, Over.associator_hom_left_fst_assoc, ExponentiableMorphism.pushforwardId_hom_counit, Limits.pullbackConeEquivBinaryFan_unitIso, Pseudofunctor.presheafHomObjHomEquiv_symm_apply, Over.isMonHom_pullbackFst_id_right, over_toGrothendieck_eq_toGrothendieck_comap_forget, Over.pullback_obj_hom, FunctorToTypes.instIsCofilteredElementsOverFromOverFunctor, Over.forgetAdjStar_unit_app_left, Pseudofunctor.isPrestackFor_iff_isSheafFor', Over.mapFunctor_map, Over.mapCongr_rfl, isEventuallyConstant_of_isNoetherianObject, GrothendieckTopology.overMapPullback_id_comp, Over.tensorObj_left, MonoOver.faithful_exists, isNoetherianObject_iff_isEventuallyConstant, Types.monoOverEquivalenceSet_counitIso, instIsCocontinuousOverLeftDiscretePUnitIteratedSliceForwardOver, CostructuredArrow.ofCostructuredArrowProjEquivalence.inverse_obj_left_left, Over.prodComparisonIso_pullback_inv_left_fst_snd', toOverUnitPullback_hom_app_left, ExponentiableMorphism.coev_ev, subterminalsEquivMonoOverTerminal_functor_obj_obj, GrothendieckTopology.pseudofunctorOver_mapId_inv_toNatTrans_app_val_app, instIsDenseSubsiteOverLeftDiscretePUnitOverInverseIteratedSliceEquiv, Over.Ξ΅_pullback_left, ChosenPullbacksAlong.pullbackComp_hom_counit_assoc, isArtinianObject_iff_isEventuallyConstant, Over.coprod_map_app, Limits.colimit.toOver_pt, MonoOver.faithful_map, Presheaf.subsingleton_iff_isSeparatedFor, Over.liftCone_pt, ChosenPullbacksAlong.unit_pullbackId_hom_app_assoc, ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd_assoc, ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst_assoc, TopCat.Presheaf.generateEquivalenceOpensLe_inverse'_map, Over.homMk_comp, MonoOver.hasLimitsOfSize, GrothendieckTopology.pseudofunctorOver_mapId_hom_toNatTrans_app_val_app, subterminals_to_monoOver_terminal_comp_forget, Over.hasLimits, AlgebraicGeometry.Scheme.restrictFunctor_obj_hom, HomotopicalAlgebra.instIsStableUnderRetractsOverWeakEquivalences, AlgebraicGeometry.Scheme.instFaithfulEtaleOverForget, AlgebraicGeometry.Scheme.IdealSheafData.subschemeFunctor_map, CostructuredArrow.ofCommaFstEquivalenceInverse_obj_hom, Subobject.representative_arrow, ExponentiableMorphism.homEquiv_apply_eq, Over.associator_hom_left_snd_snd, Over.associator_inv_left_snd_assoc, Over.coprodObj_map, toOverUnitPullback_inv_app_left, GrothendieckTopology.overMapPullbackCongr_inv_app_val_app, ChosenPullbacksAlong.unit_pullbackId_hom_assoc, ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst, GrothendieckTopology.over_forget_coverPreserving, ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd_assoc, Under.opEquivOpOver_inverse_map, AlgebraicGeometry.isCommMonObj_of_isProper_of_isIntegral_tensorObj_of_isAlgClosed, Over.iteratedSliceForward_obj, Functor.toOver_comp_forget, Over.postEquiv_functor, Over.coreHomEquivToOverSections_homEquiv, Over.whiskerLeft_left_snd, Pseudofunctor.IsPrestackFor.nonempty_fullyFaithful, Over.liftCocone_pt, Subfunctor.equivalenceMonoOver_counitIso, toOver_map, WithTerminal.coneEquiv_counitIso_hom_app_hom, presheafHom_map_app_op_mk_id, Limits.diagonal_pullback_fst, Over.iteratedSliceForwardNaturalityIso_inv_app, Over.isLeftAdjoint_post, ChosenPullbacksAlong.Over.associator_hom_left_fst_assoc, forgetAdjToOver_counit_app, CostructuredArrow.costructuredArrowToOverEquivalence.inverse_map, MorphismProperty.baseChange_obj, MonoOver.mono_obj_hom, Over.ConstructProducts.conesEquivFunctor_obj_Ο_app, Sieve.overEquiv_iff, ChosenPullbacksAlong.Over.tensorHom_left_snd, Over.opEquivOpUnder_functor_obj, AlgebraicGeometry.Scheme.AffineZariskiSite.restrictIsoSpec_inv_app, AlgebraicGeometry.instFaithfulOverSchemePullbackOfSurjectiveOfFlatOfLocallyOfFinitePresentation, HomotopicalAlgebra.fibrations_over_iff, MonoOver.instIsClosedUnderLimitsOfShapeOverIsMono, Over.ConstructProducts.conesEquivInverse_map_hom, Over.iteratedSliceForwardIsoPost_hom_app, Over.mono_of_mono_left, Over.mapForget_eq, ExponentiableMorphism.unit_pushforwardComp_hom_assoc, WithTerminal.coneEquiv_inverse_obj_pt_right_as, Over.lift_map, Over.tensorObj_hom, toOverUnit_obj_hom, Over.postAdjunctionLeft_counit_app_left, Over.hasLimitsOfShape_of_isConnected, Limits.pullbackConeEquivBinaryFan_inverse_map_hom, TopCat.Presheaf.generateEquivalenceOpensLe_inverse, Over.mapComp_inv_app_left, Pseudofunctor.sheafHom_val, Over.instHasColimits, ChosenPullbacksAlong.Over.associator_inv_left_fst_fst_assoc, MonoOver.isIso_iff_isIso_left, ChosenPullbacksAlong.Over.associator_hom_left_snd_snd_assoc, HomotopicalAlgebra.weakEquivalences_over_def, MonoOver.instIsIsoLeftDiscretePUnitHomFullSubcategoryOverIsMono, WithTerminal.coneEquiv_functor_map_hom, ChosenPullbacksAlong.Over.tensorHom_left, Presheaf.isSheaf_iff_isLimit_pretopology, essentiallySmall_monoOver_iff_small_subobject, CostructuredArrow.ofCommaFstEquivalenceInverse_map_left_right
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instCategoryUnder π | CompOp | 272 mathmath: CommRingCat.tensorProd_map_right, Limits.Cone.toUnder_pt, StructuredArrow.instFullUnderToUnder, StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_left, Limits.PreservesColimitsOfSize.underPost, StructuredArrow.ofCommaSndEquivalenceFunctor_map_right, StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_right_right, IsGrothendieckAbelian.IsPresentable.injectivityβ.F_obj, Under.postComp_inv_app_right, StructuredArrow.ofDiagEquivalence.inverse_map_right, StructuredArrow.ofCommaSndEquivalence_functor, Under.forgetMapInitial_inv_app, Under.post_comp, WithInitial.isColimitEquiv_apply_desc_right, Under.equivalenceOfIsInitial_counitIso, WithInitial.coconeEquiv_functor_obj_pt, StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_right_left_as, Under.postCongr_inv_app_right, StructuredArrow.toUnder_obj_left, Under.mapIso_functor, IsGrothendieckAbelian.IsPresentable.injectivityβ.g_app, Under.instHasLimitsOfShape, Limits.pushoutCoconeEquivBinaryCofan_inverse_obj, Limits.pushoutCoconeEquivBinaryCofan_functor_obj, WithInitial.coconeEquiv_inverse_obj_pt_right, Limits.pushoutCoconeEquivBinaryCofan_unitIso, MorphismProperty.instIsClosedUnderIsomorphismsUnderUnderObjOfRespectsIso, CommRingCat.toAlgHom_comp, StructuredArrow.ofDiagEquivalence.functor_obj_right_right, Under.equivalenceOfIsInitial_functor, WithInitial.isColimitEquiv_symm_apply_desc, Limits.Cocone.underPost_ΞΉ_app, instHasColimitsOfShapeUnderOfWithInitial, Over.opEquivOpUnder_unitIso, Under.epi_of_epi_right, Under.liftCone_pt, WithInitial.liftFromUnderComp_inv_app, StructuredArrow.ofDiagEquivalence.inverse_obj_right, Under.forget_faithful, Under.mapCongr_inv_app, Under.pushoutIsLeftAdjoint, StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_left_as, MorphismProperty.ind_iff_ind_underMk, Under.mapFunctor_obj, instHasColimitsOfSizeUnder, Under.pushout_map, Under.lift_obj, WithInitial.coconeEquiv_inverse_obj_pt_hom, Limits.pushoutCoconeEquivBinaryCofan_inverse_map_hom, CommRingCat.Under.preservesFiniteLimits_of_flat, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right_assoc, StructuredArrow.ofCommaSndEquivalence_unitIso, Under.postAdjunctionRight_unit_app_right, StructuredArrow.ofCommaSndEquivalence_counitIso, Under.map_map_right, Over.opEquivOpUnder_inverse_obj, Limits.Cone.toStructuredArrowCompToUnderCompForget_hom_app, AlgHom.toUnder_comp, StructuredArrow.ofDiagEquivalence.inverse_obj_hom, Under.map_obj_right, Under.post_obj, StructuredArrow.ofDiagEquivalence.functor_obj_right_hom, commAlgCatEquivUnder_functor_obj, StructuredArrow.ofCommaSndEquivalenceInverse_map_right_left, Under.eqToHom_right, CommRingCat.Under.instPreservesFiniteLimitsUnderTensorProdOfFlatCarrier, Under.mapId_inv, Enriched.FunctorCategory.coneFunctorEnrichedHom_Ο_app, StructuredArrow.ofDiagEquivalence.functor_map_right_right, StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_left_as, Presheaf.functorEnrichedHomCoyonedaObjEquiv_naturality, WithInitial.coconeEquiv_counitIso_inv_app_hom, CommRingCat.Under.instPreservesLimitsOfShapeUnderWalkingParallelPairTensorProdOfFlatCarrier, MorphismProperty.under_eq_inverseImage, WithInitial.commaFromUnder_map_left, NatTrans.instIsClosedUnderColimitsOfShapeUnderFunctorCoequifiberedHomDiscretePUnitOfHasProductsOfShapeHom, Limits.Cone.toStructuredArrow_comp_toUnder_comp_forget, Under.costar_obj_left, Under.isoMk_inv_right, Under.mapPushoutAdj_unit_app, StructuredArrow.ofCommaSndEquivalenceFunctor_map_left, Under.instIsEquivalenceMapOfIsIso, WithInitial.coconeEquiv_functor_obj_ΞΉ_app_star, Over.opEquivOpUnder_inverse_map, Under.liftCocone_ΞΉ_app, Under.post_map, AlgEquiv.toUnder_trans, WithInitial.coconeEquiv_unitIso_hom_app_hom_right, Functor.essImage_underPost, Under.instFaithfulObjPost, Under.map_obj_hom, CommRingCat.Under.tensorProdEqualizer_ΞΉ, Under.instEssSurjObjPostOfFull, CommRingCat.Under.instPreservesFiniteProductsUnderPushout, CommRingCat.toAlgHom_id, Under.mono_iff_mono_right, WithInitial.liftFromUnder_obj_obj, StructuredArrow.isEquivalence_toUnder, StructuredArrow.ofStructuredArrowProjEquivalence.functor_map_right_right, Under.forgetCone_pt, StructuredArrow.ofCommaSndEquivalenceFunctor_obj_right, Under.postEquiv_counitIso, Under.postComp_hom_app_right, Limits.PreservesFiniteColimits.underPost, WithInitial.coconeEquiv_functor_map_hom, Under.isoMk_hom_right, StructuredArrow.ofDiagEquivalence.functor_obj_right_left_as, algebraEquivUnder_inverse, WithInitial.coconeEquiv_inverse_obj_pt_left_as, underToAlgebra_obj_A, Under.mapCongr_hom_app, AlgEquiv.toUnder_inv_right_apply, StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_hom, Limits.Cone.mapConeToUnder_inv_hom, StructuredArrow.toUnder_map_right, Under.instIsRightAdjointForget, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right_assoc, Under.mapFunctor_map, Under.liftCone_Ο_app, Under.instIsLeftAdjointCostar, IsGrothendieckAbelian.IsPresentable.injectivityβ.F_map, Under.forgetMapInitial_hom_app, Limits.pushoutCoconeEquivBinaryCofan_functor_map_hom, WithInitial.coconeEquiv_inverse_obj_ΞΉ_app_right, CommRingCat.monoidAlgebra_map, MorphismProperty.instFullUnderTopUnderForget, WithInitial.coconeEquiv_functor_obj_ΞΉ_app_of, Under.mapComp_hom, StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_hom, Under.opEquivOpOver_functor_obj, WithInitial.commaFromUnder_obj_hom_app, WithInitial.commaFromUnder_obj_right, Under.forget_map, commAlgCatEquivUnder_counitIso, StructuredArrow.instFaithfulUnderToUnder, isCardinalFiltered_under, Under.equivalenceOfIsInitial_unitIso, Under.isLeftAdjoint_post, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right, Over.opEquivOpUnder_counitIso, commAlgCatEquivUnder_inverse_obj_carrier, CommRingCat.Under.instPreservesLimitUnderDiscreteFunctorTensorProdOfFinite, Under.mapIso_inverse, Functor.toUnder_comp_forget, StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_right, AlgEquiv.toUnder_hom_right_apply, preservesFilteredColimits_coyoneda, StructuredArrow.ofStructuredArrowProjEquivalence.inverse_map_right_right, Enriched.FunctorCategory.functorEnrichedComp_app, commAlgCatEquivUnder_unitIso, CommRingCat.isFinitelyPresentable_under, Under.instIsEquivalenceObjPost, algebraEquivUnder_unitIso, underToAlgebra_obj_a, algebraToUnder_obj, WithInitial.commaFromUnder_map_right, StructuredArrow.ofCommaSndEquivalenceInverse_obj_hom, Enriched.FunctorCategory.functorEnrichedHom_obj, Under.postMap_app, Functor.toUnder_obj_right, Under.hom_right_inv_right, Under.mapId_hom, Under.postEquiv_inverse, StructuredArrow.toUnder_obj_hom, algebraEquivUnder_counitIso, Under.postCongr_hom_app_right, Enriched.FunctorCategory.instHasEnrichedHomUnderCompMapForget, MorphismProperty.Under.forget_comp_forget_map, StructuredArrow.ofCommaSndEquivalenceInverse_map_right_right, CommRingCat.tensorProdIsoPushout_app, Under.mapId_eq, Under.pushout_obj, WithInitial.commaFromUnder_obj_left, Limits.IsColimit.pushoutCoconeEquivBinaryCofanFunctor_desc_right, Under.instHasLimits, IsFiltered.under, commAlgCatEquivUnder_inverse_map, Under.hasColimit_of_hasColimit_liftFromUnder, Under.forget_obj, Under.liftCocone_pt, WithInitial.coconeEquiv_inverse_map_hom_right, CommRingCat.Under.instPreservesFiniteProductsUnderTensorProd, Under.mapForget_eq, underToAlgebra_map_f, Under.instFullObjPostOfFaithful, Under.final_forget, preservesColimit_coyoneda_of_finitePresentation, Functor.toUnder_map_right, Under.mono_of_mono_right, Under.mapPushoutAdj_counit_app, Under.mapComp_eq, WithInitial.liftFromUnderComp_hom_app, StructuredArrow.ofCommaSndEquivalenceFunctor_obj_left, StructuredArrow.ofDiagEquivalence.functor_obj_hom, CommRingCat.Under.equalizerFork_ΞΉ, WithInitial.coconeEquiv_counitIso_hom_app_hom, Limits.Cone.toUnder_Ο_app, Under.postAdjunctionLeft_counit_app, Under.inv_right_hom_right, WithInitial.liftFromUnder_map_app, Under.mapComp_inv, MorphismProperty.underObj_ind_eq_ind_underObj, commAlgCatEquivUnder_functor_map, StructuredArrow.ofDiagEquivalence.inverse_obj_left_as, Under.hom_right_inv_right_assoc, Under.locallySmall, CommRingCat.instIsLeftAdjointCommMonCatUnderMonoidAlgebra, CommRingCat.monoidAlgebra_obj, Limits.Cone.mapConeToUnder_hom_hom, Under.opEquivOpOver_inverse_obj, Under.costar_map_left, Under.equivalenceOfIsInitial_inverse_map, StructuredArrow.ofCommaSndEquivalence_inverse, Under.opEquivOpOver_counitIso, StructuredArrow.toUnder_map_left, WithInitial.liftFromUnder_obj_map, Enriched.FunctorCategory.functorHomEquiv_apply_app, Under.mkIdInitial_to_right, Under.mono_homMk, Under.equivalenceOfIsInitial_inverse_obj, Under.costar_obj_hom, StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_right_left_as, Limits.PreservesColimitsOfShape.underPost, Under.postAdjunctionRight_counit_app_right, Limits.pushoutCoconeEquivBinaryCofan_counitIso, isFinitelyPresentable, Over.opEquivOpUnder_functor_map, Under.postEquiv_functor, Under.lift_map, Under.hasLimit_of_hasLimit_comp_forget, Under.opEquivOpOver_unitIso, StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_hom, StructuredArrow.instEssSurjUnderToUnder, Under.inv_right_hom_right_assoc, Limits.Cone.toStructuredArrowCompToUnderCompForget_inv_app, IsGrothendieckAbelian.IsPresentable.injectivityβ.hf, Under.opEquivOpOver_functor_map, Under.epi_homMk, Under.postEquiv_unitIso, StructuredArrow.ofCommaSndEquivalenceInverse_obj_left_as, algebraToUnder_map, Limits.instPreservesFilteredColimitsOfSizeUnderForget, CommRingCat.Under.instPreservesLimitUnderWalkingParallelPairParallelPairTensorProdOfFlatCarrier, Under.id_right, algebraEquivUnder_functor, Under.homMk_comp, Under.postAdjunctionLeft_unit_app, StructuredArrow.ofDiagEquivalence.functor_obj_left_as, Enriched.FunctorCategory.functorEnrichedHom_map, StructuredArrow.toUnder_obj_right, CommRingCat.preservesFilteredColimits_coyoneda, Under.isRightAdjoint_post, WithInitial.coconeEquiv_unitIso_inv_app_hom_right, Under.opEquivOpOver_inverse_map, Under.preservesLimitsOfSize_map, Limits.Cocone.underPost_pt, CommRingCat.preservesColimit_coyoneda_of_finitePresentation, Under.forgetCone_Ο_app, StructuredArrow.ofStructuredArrowProjEquivalence.inverse_obj_right_hom, IsGrothendieckAbelian.IsPresentable.injectivityβ.epi_f, StructuredArrow.ofCommaSndEquivalenceFunctor_obj_hom, Over.opEquivOpUnder_functor_obj, CommRingCat.Under.equalizer_comp, Under.forget_reflects_iso, CommRingCat.Under.equalizerFork'_ΞΉ, StructuredArrow.ofStructuredArrowProjEquivalence.functor_obj_hom, StructuredArrow.ofCommaSndEquivalenceInverse_obj_right_right, Enriched.FunctorCategory.functorEnrichedId_app, Under.comp_right, MorphismProperty.instFaithfulUnderTopUnderForget, Under.faithful_pushout, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right
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