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Essentially Algebraic Descriptionsof Locally Presentable Categories - Couverture souple

Dzierzon, Christian

 
9783836464161: Essentially Algebraic Descriptionsof Locally Presentable Categories
Couverture souple
ISBN 10 : 3836464160 ISBN 13 : 9783836464161
Editeur : VDM Verlag Dr. Müller, 2008

Synopsis

Local presentability has turned out to be one of the most fruitful concepts in category theory. The fact, that a category is locally finitely presentable iff it is equivalent to the category of models of some essentially algebraic, finitary theory, is widely known. Unfortunately, the existing approaches in literature are either unsatisfactory - with respect to existing examples and to the number of sorts needed - or even wrong. This thesis provides an intuitive proof of the mentioned fact, which covers existing examples, and can be generalized to the non-finitary case under mild assumptions. In addition to that it presents a new approach to the known characterization of quasivarieties. A non-trivial example is given by the category of coalgebras for a polynomial set-endofunctor, which turns out to be equivalent to some variety of unary algebras without equations. Moreover, polynomial set-endofunctors are characterized by the property that the corresponding category of coalgebras is concretely equivalent to some presheaf category.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

Local presentability has turned out to be one of the most fruitful concepts in category theory. The fact, that a category is locally finitely presentable iff it is equivalent to the category of models of some essentially algebraic, finitary theory, is widely known. Unfortunately, the existing approaches in literature are either unsatisfactory - with respect to existing examples and to the number of sorts needed - or even wrong. This thesis provides an intuitive proof of the mentioned fact, which covers existing examples, and can be generalized to the non-finitary case under mild assumptions. In addition to that it presents a new approach to the known characterization of quasivarieties. A non-trivial example is given by the category of coalgebras for a polynomial set-endofunctor, which turns out to be equivalent to some variety of unary algebras without equations. Moreover, polynomial set-endofunctors are characterized by the property that the corresponding category of coalgebras is concretely equivalent to some presheaf category.

Biographie de l'auteur

geboren 9. September 1976Abitur 1996Studium der Mathematik 1997-20022005 Promotion in Mathematikseit 2005 in der Versicherungswirtschaft tätig

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
VDM Verlag Dr. Müller
Date d'édition
2008
Langue
anglais
ISBN 10 
3836464160
ISBN 13 
9783836464161
Reliure
Broché
Nombre de pages
152
Coordonnées du fabricant
non disponible
Personne responsable
non disponible