Functorial semantics of topological theories

Document Type: Research Paper

Author

Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Technicka 2896/2, 616 69 Brno, Czech Republic

Abstract

Following the categorical approach to universal algebra through algebraic theories, proposed by F.~W.~Lawvere in his PhD thesis, this paper aims at introducing a similar setting for general topology. The cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. We introduce the quasicategory of catalg topological theories and consider its functorial relationships with the quasicategory of the categories of models, in order to provide convenient means for studying topological structures via the properties of their corresponding theories.

Keywords


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