Applied Categorical Structures – Official Blog

by Šlapal, Josef

We introduce and study a concept of a convergence structure on a concrete category. The concept is based on using certain generalized filters for expressing the convergence. Some basic properties of the convergence structures are discussed. In particular, we study convergence separation and convergence compactness and investigate relationships between the convergence structures and the usual closure operators on categories.

DOI: 10.1007/s10485-007-9109-0
Online Date: 9/27/2007
Print publication date: 8/1/2008
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by Hegazi, A. S.; Ismail, F.; Elsofy, M. M.

The induction theory for a Hopf group coalgebra is outlined. Given a Hopf group coalgebra H, the notions of a quotient Hopf group coalgebra and group coisotropic quantum subgroup of H are introduced. The properties of (co)induced representations are studied and the geometric interpretation and simplicity theory of such representations are given.

DOI: 10.1007/s10485-007-9099-y
Online Date: 9/7/2007
Print publication date: 4/1/2008
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by Clementino, Maria Manuel; Hofmann, Dirk; Stubbe, Isar

Exponentiable functors between quantaloid-enriched categories are characterized in elementary terms. The proof goes as follows: the elementary conditions on a given functor translate into existence statements for certain adjoints that obey some lax commutativity; this, in turn, is precisely what is needed to prove the existence of partial products with that functor; so that the functor’s exponentiability follows from the works of Niefield (J. Pure Appl. Algebra 23:147–167, 1982) and Dyckhoff and Tholen (J. Pure Appl. Algebra 49:103–116, 1987).

DOI: 10.1007/s10485-007-9104-5
Online Date: 9/7/2007
Print publication date: 2/1/2009
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