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Title: Universal objects in quasiconstructs (English)
Author: Rother, R.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 41
Issue: 1
Year: 2000
Pages: 25-39
Category: math
Summary: The general theory of J'onsson-classes is generalized to strongly smooth quasiconstructs in such a way that it also allows the construction of universal categories. One example of the theory is the existence of a concrete universal category over every base category. Properties are given which are (under certain conditions) equivalent to the existence of homogeneous universal objects. Thereby, we disprove the existence of a homogeneous {\it C\/}-universal category. The notion of homogeneity is strengthened to extremal homogeneity. Extremally homogeneous universal objects, for which additionally every morphism between smaller subobjects is extendable to an endomorphism, are constructed in so called extremally smooth quasiconstructs. (English)
Keyword: universal object
Keyword: universal category
Keyword: smooth category
Keyword: homogeneous
Keyword: J'onsson class
Keyword: special structure
MSC: 18A40
MSC: 18B15
idZBL: Zbl 1034.18005
idMR: MR1756924
Date available: 2009-01-08T18:58:08Z
Last updated: 2012-04-30
Stable URL:
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