Publication detail

Functorial semantics of topological theories

Solovjovs Sergejs

Original Title

Functorial semantics of topological theories

English Title

Functorial semantics of topological theories

Type

journal article in Web of Science

Language

en

Original 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 categorically-algebraic (catalg) 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.

English 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 categorically-algebraic (catalg) 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

Algebra, Algebraic theory, Comma category, Categorically-algebraic topology, Poslat topology, Powerset theory, Topological system, Topological theory, Variety

RIV year

2015

Released

01.11.2015

Publisher

UNIV SISTAN & BALUCHESTAN

Location

Iran

Pages from

1

Pages to

43

Pages count

42

Documents

BibTex


@article{BUT126461,
  author="Sergejs {Solovjovs}",
  title="Functorial semantics of topological theories",
  annote="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 categorically-algebraic (catalg) 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.",
  address="UNIV SISTAN & BALUCHESTAN",
  chapter="126461",
  howpublished="print",
  institution="UNIV SISTAN & BALUCHESTAN",
  number="5",
  volume="12",
  year="2015",
  month="november",
  pages="1--43",
  publisher="UNIV SISTAN & BALUCHESTAN",
  type="journal article in Web of Science"
}