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A topological theory of (T,V)-categories

A topological theory of (T,V)-categories

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Title: A topological theory of (T,V)-categories
Author: Sozubek, Serdar
Abstract: Lawvere's notion of completeness for quantale-enriched categories has been extended to the theory of lax algebras under the name of L-completeness. In this work we introduce the corresponding morphism concept and examine its properties. We explore some important relativized topological concepts like separation, density, compactness and compactification with respect to L-complete morphisms. We show that separated L-complete morphisms belong to a factorization system. Moreover, we investigate relativized topological concepts with respect to maps that preserve L-closure which is the natural symmetrized closure for lax algebras. We provide concrete characterizations of Zariski closure and Zariski compactness for approach spaces.
Type: Electronic Thesis or Dissertation
Rights: Author owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
URI: http://hdl.handle.net/10315/32010

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