Previous |  Up |  Next

Article

Title: Totality of colimit closures (English)
Author: Börger, Reinhard
Author: Tholen, Walter
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 32
Issue: 4
Year: 1991
Pages: 761-768
.
Category: math
.
Summary: Adámek, Herrlich, and Reiterman showed that a cocomplete category $\Cal A$ is cocomplete if there exists a small (full) subcategory $\Cal B$ such that every $\Cal A$-object is a colimit of $\Cal B$-objects. The authors of the present paper strengthened the result to totality in the sense of Street and Walters. Here we weaken the hypothesis, assuming only that the colimit closure is attained by transfinite iteration of the colimit closure process up to a fixed ordinal. This requires some investigations on generalized notions of generators. (English)
Keyword: cocomplete category
Keyword: (almost-)$\Cal E$-generator
Keyword: colimit closure
Keyword: cointersection
Keyword: total category
MSC: 18A20
MSC: 18A30
MSC: 18A35
MSC: 18A40
MSC: 18B99
idZBL: Zbl 0760.18002
idMR: MR1159823
.
Date available: 2009-01-08T17:48:58Z
Last updated: 2012-04-30
Stable URL: http://hdl.handle.net/10338.dmlcz/118456
.
Reference: [1] Adámek J., Herrlich H., Reiterman J.: Cocompleteness almost implies completeness. Proc. Conf. Cat. Top. Prague, World Scientific, Singapore, 1989.. MR 1047905
Reference: [2] Börger R.: Making factorizations compositive.Comment. Math. Univ. Carolinae 32 (1991), 749-759. MR 1159822
Reference: [3] Börger R., Tholen W.: Concordant-dissonant and monotone-light.Proceedings of the International Conference on Categorical Topology, Toledo (Ohio), 1983, Sigma Series in Pure Mathematics 5 (1984), 90-107. MR 0785013
Reference: [4] Börger R., Tholen W.: Total categories and solid functors.Canad. J. Math. 42 (1990), 213-229. MR 1051726
Reference: [5] Börger R., Tholen W.: Strong, regular, and dense generators.Cahiers Topologie Géom. Différentielle Catégoriques, to appear. MR 1158111
Reference: [6] Day B.: Further criteria for totality.Cahiers Topologie Géom. Différentielle Catégoriques 28 (1987), 77-78. Zbl 0626.18001, MR 0903153
Reference: [7] Isbell J.R.: Structure of categories.Bull. Amer. Math. Soc. 72 (1966), 619-655. Zbl 0142.25401, MR 0206071
Reference: [8] Kelly G.M.: Monomorphisms, epimorphisms, and pullbacks.J. Austral. Math. Soc. A9 (1969), 124-142. MR 0240161
Reference: [9] Kelly G.M.: A survey on totality for enriched and ordinary categories.Cahiers Topologie Géom. Différentielle Catégoriques 27 (1986), 109-131. MR 0850527
Reference: [10] Kunen K.: Set theory.Studies in Logic and the Foundation of Mathematics 102, North-Holland, Amsterdam, 1980. Zbl 0960.03033, MR 0597342
Reference: [11] MacDonald J., Stone A.: Essentially monadic adjunctions.Lecture Notes in Mathematics 962, Springer, Berlin (1982), 167-174. Zbl 0498.18003, MR 0682954
Reference: [12] Pareigis B.: Categories and Functors.Academic Press, London, 1970. Zbl 0211.32402, MR 0265428
Reference: [13] Street R., Walters R.: Yoneda structures on 2-categories.J. Algebra 50 (1978), 350-379. Zbl 0401.18004, MR 0463261
.

Files

Files Size Format View
CommentatMathUnivCarolRetro_32-1991-4_19.pdf 213.5Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo