Publication detail

Functorial semantics of topological theories

Solovjovs Sergejs

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 in English

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

ISSN

1735-0654

Volume

12

Number

5

Pages from–to

1–43

Pages count

42

BIBTEX


@article{BUT126461,
  author="Sergejs {Solovjovs},
  title="Functorial semantics of topological theories",
  year="2015",
  volume="12",
  number="5",
  month="November",
  pages="1--43",
  publisher="UNIV SISTAN & BALUCHESTAN",
  address="Iran",
  issn="1735-0654"
}