Porst, Hans-Eberhard
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Porst, Hans-Eberhard
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Porst, Hans-Eberhard
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Item-typ:Veröffentlichung, Varietale und monadische Vervollständigungen(2007-08-29); ; ; Construction of varietal and monadic completions. Characterization of abstract equivalence of (manysorted) (finitary) varieties via varietal and monadic completions.Dissertation243 109 - Some of the metrics are blocked by yourconsent settings
Item-typ:Veröffentlichung, Essentially Algebraic Descriptions of Locally Presentable Categories(2005-09-06); ; ; 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 an 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 - or even wrong. Now the aim of the main part of this thesis is to give an intuitive proof of the mentioned fact, which covers existing examples, and can be generalized to the non-finitary case under mild assumptions. Here the set of sorts of such a description of a locally finitely presentable category is given by a strong generator of finitely presentables in this category. Also, this construction provides a new approach to the known characterization of quasivarieties. Further, the theory constructed for a locally finitely presentable category is some kind of clone. A non-trivial example of a locally finitely presentable category with a managable strong generator of finitely presentables is given by the category of coalgebras for a polynomial set-endofunctor. In the second part of this dissertation we show that this category is even equivalent to some variety of unary algebras without equations. Moreover, we characterize polynomial set-endofunctors by the property that the corresponding category of coalgebras is concretely equivalent to some presheaf category. Finally, we introduce for an endofunctor the concept of polynomiality w.r.t. a family of functors, and show that - under certain assumptions - several constructions and properties can be lifted to the corresponding category of coalgebras.Dissertation234 158 - Some of the metrics are blocked by yourconsent settings
Item-typ:Veröffentlichung, Lax Algebras: A Scenic Approach(2006-12-01); ; ; Lax algebras provide a setting for the simultaneous study of a wide range of topological structures. We propose scenes as an axiomatic setting for the study of lax algebras.After collecting basic facts on order-enriched categories, we present various methods to construct (lax) extensions of functors. We define lax algebras in a scenic context and present various examples. Exactness properties of categories of lax algebras are discussed. Here, special emphasis is put on strict and costrict morphisms, which provide a generalization of proper and open maps of topological spaces. Using strict morphisms a notion of compactness for lax algebras is discussed. For this notion of compactness a general Tychonoff-type theorem is proved.Dissertation318 145