Profinite categories and semidirect products

• Type: Article in International Scientific Journal
• Date: 1998

Authors

Almeida, J (Author) FCUP; Weil, P (Author) Other

Journal

Title: Journal of Pure and Applied Algebra

Vol. 123

Pages: 1-50

ISSN: 0022-4049

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 54 Citations

Scopus - 55 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-001-9CY

DOI: 10.1016/s0022-4049(96)00083-7

Abstract (EN): After developing a theory of implicit operations and proving an analogue of Reiterman's theorem for categories, this paper addresses two complementary questions for semidirect products and two-sided semidirect products of pseudovarieties of semigroups: to determine when a pseudoidentity is valid in it, and to find a basis of pseudoidentities. The first question involves looking into the structure of relatively free profinite objects whereas, for the second question, a general approach is presented which is sufficiently powerful to allow the calculation of many semidirect products. A systematic translation of bases of pseudoidentities of pseudovarieties of categories into characterizations of semidirect products of pseudovarieties of semigroups is given. The latter characterizations, of a syntactic nature, are not effective but may in many cases be reduced to effective characterizations. Several known results are derived as examples - including a syntactic proof of a generalization of the Delay Theorem - and further new applications are obtained using these techniques. (C) 1998 Elsevier Science B.V.

Language: English

Type (Professor's evaluation): Scientific