100_related-properties.sql

INSERT INTO related_properties (property_id, related_property_id)
VALUES
('small', 'essentially small'),
('small', 'locally small'),
('locally small', 'small'),
('locally small', 'locally essentially small'),
('locally essentially small', 'locally small'),
('essentially small', 'small'),
('essentially small', 'locally essentially small'),
('cartesian closed', 'finite products'),
('cartesian closed', 'locally cartesian closed'),
('cocartesian coclosed', 'finite coproducts'),
('cocartesian coclosed', 'locally cocartesian coclosed'),
('locally cartesian closed', 'cartesian closed'),
('locally cocartesian coclosed', 'cocartesian coclosed'),
('zero morphisms', 'preadditive'),
('zero morphisms', 'pointed'),
('preadditive', 'additive'),
('additive', 'preadditive'),
('additive', 'finite products'),
('additive', 'finite coproducts'),
('additive', 'biproducts'),
('biproducts', 'zero morphisms'),
('biproducts', 'finite products'),
('biproducts', 'finite coproducts'),
('abelian', 'additive'),
('abelian', 'kernels'),
('abelian', 'cokernels'),
('abelian', 'normal'),
('abelian', 'conormal'),
('finitely complete', 'complete'),
('finitely complete', 'finite products'),
('finitely complete', 'equalizers'),
('finitely cocomplete', 'cocomplete'),
('finitely cocomplete', 'finite coproducts'),
('finitely cocomplete', 'coequalizers'),
('pointed', 'initial object'),
('pointed', 'terminal object'),
('locally finitely presentable', 'cocomplete'),
('locally finitely presentable', 'locally presentable'),
('locally finitely presentable', 'locally strongly finitely presentable'),
('locally finitely presentable', 'locally ℵ₁-presentable'),
('locally finitely presentable', 'finitely accessible'),
('locally finitely presentable', 'locally finitely multi-presentable'),
('locally strongly finitely presentable', 'locally finitely presentable'),
('locally strongly finitely presentable', 'multi-algebraic'),
('locally strongly finitely presentable', 'generalized variety'),
('locally presentable', 'cocomplete'),
('locally presentable', 'locally finitely presentable'),
('locally presentable', 'locally ℵ₁-presentable'),
('locally presentable', 'accessible'),
('locally presentable', 'locally multi-presentable'),
('locally presentable', 'locally poly-presentable'),
('locally ℵ₁-presentable', 'cocomplete'),
('locally ℵ₁-presentable', 'locally finitely presentable'),
('locally ℵ₁-presentable', 'locally presentable'),
('locally ℵ₁-presentable', 'ℵ₁-accessible'),
('elementary topos', 'Grothendieck topos'),
('elementary topos', 'cartesian closed'),
('elementary topos', 'finitely complete'),
('elementary topos', 'subobject classifier'),
('elementary topos', 'natural numbers object'),
('Grothendieck topos', 'elementary topos'),
('natural numbers object', 'elementary topos'),
('natural numbers object', 'finite products'),
('initial object', 'finite coproducts'),
('initial object', 'multi-initial object'),
('terminal object', 'finite products'),
('terminal object', 'multi-terminal object'),
('complete', 'equalizers'),
('complete', 'products'),
('complete', 'multi-complete'),
('equalizers', 'finitely complete'),
('equalizers', 'coreflexive equalizers'),
('equalizers', 'kernels'),
('coequalizers', 'finitely cocomplete'),
('coequalizers', 'reflexive coequalizers'),
('coequalizers', 'cokernels'),
('kernels', 'zero morphisms'),
('kernels', 'equalizers'),
('kernels', 'normal'),
('cokernels', 'zero morphisms'),
('cokernels', 'coequalizers'),
('cokernels', 'conormal'),
('cocomplete', 'coequalizers'),
('cocomplete', 'coproducts'),
('cocomplete', 'multi-cocomplete'),
('products', 'complete'),
('products', 'finite products'),
('products', 'powers'),
('coproducts', 'cocomplete'),
('coproducts', 'finite coproducts'),
('coproducts', 'copowers'),
('finite products', 'products'),
('finite products', 'finite powers'),
('finite products', 'binary products'),
('finite products', 'terminal object'),
('finite coproducts', 'coproducts'),
('finite coproducts', 'binary coproducts'),
('finite coproducts', 'initial object'),
('finite coproducts', 'finite copowers'),
('binary products', 'finite products'),
('binary products', 'binary powers'),
('binary coproducts', 'finite coproducts'),
('binary coproducts', 'binary copowers'),
('countable products', 'products'),
('countable products', 'finite products'),
('countable products', 'countable powers'),
('countable coproducts', 'coproducts'),
('countable coproducts', 'finite coproducts'),
('countable coproducts', 'countable copowers'),
('cofiltered limits', 'cofiltered'),
('cofiltered limits', 'complete'),
('cofiltered limits', 'directed limits'),
('cofiltered limits', 'cosifted limits'),
('filtered colimits', 'filtered'),
('filtered colimits', 'cocomplete'),
('filtered colimits', 'directed colimits'),
('filtered colimits', 'sifted colimits'),
('directed limits', 'cofiltered limits'),
('directed limits', 'complete'),
('directed colimits', 'filtered colimits'),
('directed colimits', 'cocomplete'),
('sequential limits', 'directed limits'),
('sequential colimits', 'directed colimits'),
('cogenerator', 'cogenerating set'),
('cogenerating set', 'cogenerator'),
('connected limits', 'connected'),
('connected limits', 'complete'),
('connected limits', 'cofiltered limits'),
('connected colimits', 'connected'),
('connected colimits', 'cocomplete'),
('connected colimits', 'filtered colimits'),
('strict initial object', 'initial object'),
('strict terminal object', 'terminal object'),
('discrete', 'essentially discrete'),
('essentially discrete', 'discrete'),
('finite', 'essentially finite'),
('finite', 'small'),
('finite', 'countable'),
('essentially finite', 'finite'),
('essentially finite', 'essentially small'),
('essentially finite', 'essentially countable'),
('countable', 'essentially countable'),
('countable', 'finite'),
('essentially countable', 'countable'),
('essentially countable', 'essentially finite'),
('pullbacks', 'wide pullbacks'),
('pullbacks', 'binary products'),
('pushouts', 'wide pushouts'),
('pushouts', 'binary coproducts'),
('subobject classifier', 'elementary topos'),
('subobject classifier', 'finitely complete'),
('subobject classifier', 'regular subobject classifier'),
('regular subobject classifier', 'subobject classifier'),
('regular subobject classifier', 'finitely complete'),
('quotient object classifier', 'finitely cocomplete'),
('quotient object classifier', 'regular quotient object classifier'),
('regular quotient object classifier', 'quotient object classifier'),
('regular quotient object classifier', 'finitely cocomplete'),
('distributive', 'infinitary distributive'),
('distributive', 'countably distributive'),
('distributive', 'finite products'),
('distributive', 'finite coproducts'),
('countably distributive', 'distributive'),
('countably distributive', 'infinitary distributive'),
('countably distributive', 'finite products'),
('countably distributive', 'countable coproducts'),
('infinitary distributive', 'distributive'),
('infinitary distributive', 'countably distributive'),
('infinitary distributive', 'finite products'),
('infinitary distributive', 'coproducts'),
('codistributive', 'infinitary codistributive'),
('codistributive', 'countably codistributive'),
('codistributive', 'finite products'),
('codistributive', 'finite coproducts'),
('countably codistributive', 'codistributive'),
('countably codistributive', 'infinitary codistributive'),
('countably codistributive', 'finite coproducts'),
('countably codistributive', 'countable products'),
('infinitary codistributive', 'codistributive'),
('infinitary codistributive', 'countably codistributive'),
('infinitary codistributive', 'finite coproducts'),
('infinitary codistributive', 'products'),
('exact filtered colimits', 'filtered colimits'),
('exact filtered colimits', 'finitely complete'),
('exact filtered colimits', 'cartesian filtered colimits'),
('exact cofiltered limits', 'cofiltered limits'),
('exact cofiltered limits', 'finitely cocomplete'),
('exact cofiltered limits', 'cocartesian cofiltered limits'),
('exact cofiltered limits', 'cofiltered-limit-stable epimorphisms'),
('cartesian filtered colimits', 'filtered colimits'),
('cartesian filtered colimits', 'finite products'),
('cartesian filtered colimits', 'exact filtered colimits'),
('cocartesian cofiltered limits', 'cofiltered limits'),
('cocartesian cofiltered limits', 'finite coproducts'),
('cocartesian cofiltered limits', 'exact cofiltered limits'),
('filtered-colimit-stable monomorphisms', 'exact filtered colimits'),
('filtered-colimit-stable monomorphisms', 'filtered colimits'),
('cofiltered-limit-stable epimorphisms', 'exact cofiltered limits'),
('cofiltered-limit-stable epimorphisms', 'cofiltered limits'),
('generator', 'generating set'),
('generating set', 'generator'),
('Grothendieck abelian', 'abelian'),
('Grothendieck abelian', 'cocomplete'),
('Grothendieck abelian', 'generator'),
('Grothendieck abelian', 'exact filtered colimits'),
('disjoint finite coproducts', 'finite coproducts'),
('disjoint finite coproducts', 'disjoint coproducts'),
('disjoint finite coproducts', 'extensive'),
('disjoint coproducts', 'coproducts'),
('disjoint coproducts', 'disjoint finite coproducts'),
('disjoint coproducts', 'infinitary extensive'),
('disjoint finite products', 'finite products'),
('disjoint finite products', 'disjoint products'),
('disjoint finite products', 'coextensive'),
('disjoint products', 'products'),
('disjoint products', 'disjoint finite products'),
('disjoint products', 'infinitary coextensive'),
('left cancellative', 'groupoid'),
('right cancellative', 'groupoid'),
('groupoid', 'left cancellative'),
('groupoid', 'right cancellative'),
('wide pullbacks', 'pullbacks'),
('wide pushouts', 'pushouts'),
('split abelian', 'abelian'),
('Cauchy complete', 'finitely complete'),
('Malcev', 'finitely complete'),
('co-Malcev', 'finitely cocomplete'),
('connected', 'semi-strongly connected'),
('connected', 'strongly connected'),
('connected', 'inhabited'),
('semi-strongly connected', 'connected'),
('semi-strongly connected', 'strongly connected'),
('semi-strongly connected', 'inhabited'),
('strongly connected', 'connected'),
('strongly connected', 'semi-strongly connected'),
('strongly connected', 'inhabited'),
('regular', 'finitely complete'),
('coregular', 'finitely cocomplete'),
('extensive', 'infinitary extensive'),
('extensive', 'finite coproducts'),
('extensive', 'disjoint finite coproducts'),
('infinitary extensive', 'extensive'),
('infinitary extensive', 'coproducts'),
('infinitary extensive', 'disjoint coproducts'),
('coextensive', 'infinitary coextensive'),
('coextensive', 'finite products'),
('coextensive', 'disjoint finite products'),
('infinitary coextensive', 'coextensive'),
('infinitary coextensive', 'products'),
('infinitary coextensive', 'disjoint products'),
('well-powered', 'small'),
('well-copowered', 'small'),
('unital', 'finitely complete'),
('unital', 'pointed'),
('unital', 'Malcev'),
('counital', 'finitely cocomplete'),
('counital', 'pointed'),
('counital', 'co-Malcev'),
('cosifted limits', 'complete'),
('cosifted limits', 'cofiltered limits'),
('cosifted limits', 'coreflexive equalizers'),
('cosifted limits', 'cosifted'),
('sifted colimits', 'cocomplete'),
('sifted colimits', 'filtered colimits'),
('sifted colimits', 'reflexive coequalizers'),
('sifted colimits', 'sifted'),
('sifted', 'sifted colimits'),
('sifted', 'filtered'),
('sifted', 'connected'),
('cosifted', 'cosifted limits'),
('cosifted', 'connected'),
('cosifted', 'cofiltered'),
('coreflexive equalizers', 'equalizers'),
('coreflexive equalizers', 'cosifted limits'),
('reflexive coequalizers', 'coequalizers'),
('reflexive coequalizers', 'sifted colimits'),
('direct', 'one-way'),
('direct', 'skeletal'),
('inverse', 'one-way'),
('inverse', 'skeletal'),
('one-way', 'direct'),
('one-way', 'inverse'),
('powers', 'products'),
('powers', 'countable powers'),
('powers', 'finite powers'),
('countable powers', 'countable products'),
('countable powers', 'powers'),
('countable powers', 'finite powers'),
('finite powers', 'finite products'),
('finite powers', 'powers'),
('finite powers', 'countable powers'),
('finite powers', 'binary powers'),
('copowers', 'coproducts'),
('copowers', 'countable copowers'),
('copowers', 'finite copowers'),
('countable copowers', 'countable coproducts'),
('countable copowers', 'copowers'),
('countable copowers', 'finite copowers'),
('finite copowers', 'copowers'),
('finite copowers', 'finite coproducts'),
('finite copowers', 'countable copowers'),
('finite copowers', 'binary copowers'),
('binary powers', 'finite powers'),
('binary powers', 'finite products'),
('binary copowers', 'finite copowers'),
('binary copowers', 'finite coproducts'),
('filtered', 'finitely cocomplete'),
('filtered', 'filtered colimits'),
('cofiltered', 'finitely complete'),
('cofiltered', 'cofiltered limits'),
('mono-regular', 'normal'),
('epi-regular', 'conormal'),
('normal', 'zero morphisms'),
('normal', 'mono-regular'),
('normal', 'kernels'),
('conormal', 'zero morphisms'),
('conormal', 'epi-regular'),
('conormal', 'cokernels'),
('multi-complete', 'complete'),
('multi-complete', 'multi-terminal object'),
('multi-terminal object', 'multi-complete'),
('multi-terminal object', 'terminal object'),
('multi-cocomplete', 'cocomplete'),
('multi-cocomplete', 'multi-initial object'),
('multi-initial object', 'multi-cocomplete'),
('multi-initial object', 'initial object'),
('accessible', 'finitely accessible'),
('accessible', 'ℵ₁-accessible'),
('accessible', 'locally presentable'),
('accessible', 'locally multi-presentable'),
('accessible', 'locally poly-presentable'),
('ℵ₁-accessible', 'accessible'),
('ℵ₁-accessible', 'finitely accessible'),
('ℵ₁-accessible', 'locally ℵ₁-presentable'),
('finitely accessible', 'accessible'),
('finitely accessible', 'ℵ₁-accessible'),
('finitely accessible', 'locally finitely presentable'),
('finitely accessible', 'locally finitely multi-presentable'),
('finitely accessible', 'filtered colimits'),
('locally multi-presentable', 'locally finitely multi-presentable'),
('locally multi-presentable', 'locally presentable'),
('locally multi-presentable', 'locally poly-presentable'),
('locally multi-presentable', 'accessible'),
('locally multi-presentable', 'multi-cocomplete'),
('locally multi-presentable', 'connected limits'),
('locally finitely multi-presentable', 'locally multi-presentable'),
('locally finitely multi-presentable', 'finitely accessible'),
('locally finitely multi-presentable', 'filtered colimits'),
('locally finitely multi-presentable', 'multi-cocomplete'),
('locally finitely multi-presentable', 'connected limits'),
('locally finitely multi-presentable', 'multi-algebraic'),
('locally poly-presentable', 'locally presentable'),
('locally poly-presentable', 'locally multi-presentable'),
('locally poly-presentable', 'accessible'),
('locally poly-presentable', 'wide pullbacks'),
('multi-algebraic', 'locally finitely multi-presentable'),
('multi-algebraic', 'locally strongly finitely presentable'),
('multi-algebraic', 'generalized variety'),
('multi-algebraic', 'sifted colimits'),
('multi-algebraic', 'multi-cocomplete'),
('generalized variety', 'multi-algebraic'),
('generalized variety', 'locally strongly finitely presentable'),
('generalized variety', 'sifted colimits');