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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  1. Adámek J., Herrlich H., Strecker G., Abstract and Concrete Categories, Wiley Interscience, New York, 1990. MR1051419
  2. Comfort W.W., Negrepontis S., The Theory of Ultrafilters, Springer, Berlin-Heidelberg, 1974. Zbl0298.02004MR0396267
  3. Herrlich H., Strecker G.E., Category Theory, Heldermann, Berlin, 1979. Zbl1125.18300MR0571016
  4. Jónsson B., Homogeneous universal relational systems, Math. Scand. 8 (1960), 137-142. (1960) MR0125021
  5. Kučera L., On universal concrete categories, Algebra Universalis 5 (1975), 149-151. (1975) MR0404385
  6. Negrepontis S., The Stone Space of the Saturated Boolean Algebras, Proc. Internat. Sympos. on Topology and its Applications, Herceg-Novi, August 1968. Zbl0223.06002MR0248057
  7. Rother R., Realizations of topological categories, Applied Categorical Structures, to appear. Zbl0993.18003MR1865613
  8. Trnková V., Sum of categories with amalgamated subcategory, Comment. Math. Univ. Carolinae 6.4 (1965), 449-474. (1965) MR0190208
  9. Trnková V., Universal categories, Comment. Math. Univ. Carolinae 7.2 (1966), 143-206. (1966) MR0202808
  10. Trnková V., Universal concrete categories and functors, Cahiers Topologie Géom. Différentielle Catégoriques, Vol. 34-3 (1993), 239-256. (1993) MR1239471
  11. Trnková V., Universalities, Applied Categorical Structures 2 (1994), 173-185. (1994) MR1283435

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