Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-18T01:09:30.036Z Has data issue: false hasContentIssue false
  • English
  • Français

Finitary sketches and finitely accessible categories*

Published online by Cambridge University Press:  04 March 2009

Jiří Adámek  and
Jiří Rosický
Jiří Adámek
Affiliation:
Czech Technical University, Technická 2, 166 27 Praha 6, Czech Republic
Jiří Rosický
Affiliation:
Masaryk University, Janáčkovo nám. 2a, 662 95 Brno, Czech Republic
Get access Rights & Permissions [Opens in a new window]

Abstract

Every accessible category is proved to be sketchable by a sketch with finite colimits. In contrast, a finitely accessible category is presented that cannot be sketched by a finitary sketch, i.e., a sketch with finite limits and finite colimits. Also, a category sketchable by a finitary sketch is found that is not finitely accessible.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 5 , Issue 3 , September 1995 , pp. 315 - 322
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adámek, J. and Rosický, J. (1994) Locally presentable and accessible categories, Cambridge University Press.CrossRefGoogle Scholar
Gabriel, P. and Ulmer, F. (1971) Lokal präsentierbare Kategorien. Springer-Verlag Lecture Notes in Mathematics 221.Google Scholar
Lair, C. (1981) Catégories modélables et catégories esquissables. Diagrammes 6 1–20.Google Scholar
Makkai, M. and Paré, R. (1989) Accessible categories: the foundations of categorical model theory. Contemporary Math. 104.CrossRefGoogle Scholar
Rosický, J. (1984) Categories of models. Seminarberichte Fernuniversität Hagen 19 377–413.Google Scholar
Rosický, J. (1989) Elementary categories. Arch. Math. 52 284–288.CrossRefGoogle Scholar