Essentially Algebraic Descriptionsof Locally Presentable Categories

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November 2013



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.


geboren 9. September 1976
Abitur 1996
Studium der Mathematik 1997-2002
2005 Promotion in Mathematik
seit 2005 in der Versicherungswirtschaft tätig
EAN: 9783836464161
ISBN: 3836464160
Untertitel: Paperback.
Verlag: VDM Verlag Dr. Müller e.K.
Erscheinungsdatum: November 2013
Seitenanzahl: 152 Seiten
Format: kartoniert
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