Universal objects in quasiconstructs

R. Rother

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 1, page 25-39
  • ISSN: 0010-2628

Abstract

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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 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.

How to cite

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Rother, R.. "Universal objects in quasiconstructs." Commentationes Mathematicae Universitatis Carolinae 41.1 (2000): 25-39. <http://eudml.org/doc/248607>.

@article{Rother2000,
abstract = {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 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.},
author = {Rother, R.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {universal object; universal category; smooth category; homogeneous; J'onsson class; special structure; universal object; universal category; smooth category; homogeneous object; Jónsson class; special structure},
language = {eng},
number = {1},
pages = {25-39},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Universal objects in quasiconstructs},
url = {http://eudml.org/doc/248607},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Rother, R.
TI - Universal objects in quasiconstructs
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 1
SP - 25
EP - 39
AB - 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 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.
LA - eng
KW - universal object; universal category; smooth category; homogeneous; J'onsson class; special structure; universal object; universal category; smooth category; homogeneous object; Jónsson class; special structure
UR - http://eudml.org/doc/248607
ER -

References

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