Hostname: page-component-7479d7b7d-68ccn Total loading time: 0 Render date: 2024-07-13T13:35:54.126Z Has data issue: false hasContentIssue false

Existence and Nonexistence of Regular Generators

Published online by Cambridge University Press:  20 November 2018

J. Adámek*
Affiliation:
Czech Technical University, Technická 2, Praha 6, Czechoslovakia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A total category is constructed which has no regular generator although it has an object C such that every object is a regular quotient of a copower of C.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1994

References

[AHR] Adámek, J., Herrlich, H. and Reiterman, J., Completeness almost implies cocompleteness, Proc. of Categorical Topology, Prague, 1988, World Scient. Publ., Singapore, 1989.Google Scholar
[AHS] Adámek, J., Herrlich, H. and Strecker, G. E., Abstract and concrete categories, Wiley-Interscience Publ., New York, 1990.Google Scholar
[BT] ] Börger, R. and Tholen, W., Strong, regular and dense generators, Cahiers Topol. Géom. Différentielle, to appear.Google Scholar
[BT2 Börger, J and Tholen, W., Total categories and solid functors, Canad. J. Math. 42(1990), 213229.Google Scholar
[BT3]Börger and Tholen, W., Totality of colimit closures, Comment. Math. Univ. Carolinae 32(1991), 749759.Google Scholar
[D] Day, B. J., Further criteria for totality, Cahiers Topol. Géom. Différentielle 28(1987), 7778.Google Scholar
[GU] P.Gabriel and Ulmer, P., Lokalprdsentierbare Kategorien, Springer Lecture Notes In Math. 221, Springer- Verlag, 1971.Google Scholar
[K] Kelly, G. M., A survey of totality for enrichedandordinary categories, Cahiers Topol. Géom. Différentielle 27(1986), 109131.Google Scholar
[T] Tholen, W., Note on total categories, Bull. Austral. Math. Soc. 21(1980), 169173.Google Scholar
[TRA] Trnkovä, V., Rosicky, J. and J. Adämek, Unexpected properties oflocally presentable categories, Algebra Universalis 27(1990), 153170.Google Scholar