A remark on accessible and axiomatizable categories

Jiří Adámek; Jiří Rosický

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 2, page 411-414
  • ISSN: 0010-2628

Abstract

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For categories with equalizers the concepts ``accessible'' and ``axiomatizable'' are equivalent. This results is proved under (in fact, is equivalent to) the large-cardinal Vopěnka's principle.

How to cite

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Adámek, Jiří, and Rosický, Jiří. "A remark on accessible and axiomatizable categories." Commentationes Mathematicae Universitatis Carolinae 37.2 (1996): 411-414. <http://eudml.org/doc/247887>.

@article{Adámek1996,
abstract = {For categories with equalizers the concepts ``accessible'' and ``axiomatizable'' are equivalent. This results is proved under (in fact, is equivalent to) the large-cardinal Vopěnka's principle.},
author = {Adámek, Jiří, Rosický, Jiří},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {accessible category; infinitary logic; Vopěnka's principle; accessible category; bounded category; axiomatizable category; regular cardinal; many-sorted infinitary first order theory; Vopěnka’s principle},
language = {eng},
number = {2},
pages = {411-414},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A remark on accessible and axiomatizable categories},
url = {http://eudml.org/doc/247887},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Adámek, Jiří
AU - Rosický, Jiří
TI - A remark on accessible and axiomatizable categories
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 2
SP - 411
EP - 414
AB - For categories with equalizers the concepts ``accessible'' and ``axiomatizable'' are equivalent. This results is proved under (in fact, is equivalent to) the large-cardinal Vopěnka's principle.
LA - eng
KW - accessible category; infinitary logic; Vopěnka's principle; accessible category; bounded category; axiomatizable category; regular cardinal; many-sorted infinitary first order theory; Vopěnka’s principle
UR - http://eudml.org/doc/247887
ER -

References

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  1. Adámek J., Rosický J., Locally Presentable and Accessible Categories, Cambridge Univ. Press, 1994. MR1294136
  2. Diers Y., Catégories localement multiprésentables, Arch. Math. 34 (1980), 344-356. (1980) Zbl0453.18002MR0593951
  3. Fisher E.R., Vopěnka's principle, category theory and universal algebra, personal communication, 1987. 
  4. Jech T., Set Theory, Academic Press, 1978. Zbl1007.03002MR0506523
  5. Lair C., Catégories modélables et catégories esquissables, Diagrammes 6 (1981), 1-20. (1981) Zbl0522.18008MR0684535
  6. Makkai M., Paré R., Accessible categories: the foundations of categorical model theory, Contemp. Math. 104 (1989). (1989) MR1031717
  7. Rosický J., Trnková V., Adámek J., Unexpected properties of locally presentable categories, Alg. Univ. 27 (1990), 153-170. (1990) MR1037859

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