Totality of colimit closures
Börger, Reinhard ; Tholen, Walter
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991), p. 761-768 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1991-01-01
Classification:  18A20,  18A30,  18A35,  18A40,  18B99 
@article{118456,
     author = {Reinhard B\"orger and Walter Tholen},
     title = {Totality of colimit closures},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {32},
     year = {1991},
     pages = {761-768},
     zbl = {0760.18002},
     mrnumber = {1159823},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118456}
}

Börger, Reinhard; Tholen, Walter. Totality of colimit closures. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 761-768. http://gdmltest.u-ga.fr/item/118456/

Adámek J.; Herrlich H.; Reiterman J. Cocompleteness almost implies completeness. Proc. Conf. Cat. Top. Prague, World Scientific, Singapore, 1989, . | MR 1047905

Börger R. Making factorizations compositive, Comment. Math. Univ. Carolinae 32 (1991), 749-759. (1991) | MR 1159822

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

Börger R.; Tholen W. Total categories and solid functors, Canad. J. Math. 42 (1990), 213-229. (1990) | MR 1051726

Börger R.; Tholen W. Strong, regular, and dense generators, Cahiers Topologie Géom. Différentielle Catégoriques, to appear. | MR 1158111

Day B. Further criteria for totality, Cahiers Topologie Géom. Différentielle Catégoriques 28 (1987), 77-78. (1987) | MR 0903153 | Zbl 0626.18001

Isbell J.R. Structure of categories, Bull. Amer. Math. Soc. 72 (1966), 619-655. (1966) | MR 0206071 | Zbl 0142.25401

Kelly G.M. Monomorphisms, epimorphisms, and pullbacks, J. Austral. Math. Soc. A9 (1969), 124-142. (1969) | MR 0240161

Kelly G.M. A survey on totality for enriched and ordinary categories, Cahiers Topologie Géom. Différentielle Catégoriques 27 (1986), 109-131. (1986) | MR 0850527

Kunen K. Set theory, Studies in Logic and the Foundation of Mathematics 102, North-Holland, Amsterdam, 1980. | MR 0597342 | Zbl 0960.03033

Macdonald J.; Stone A. Essentially monadic adjunctions, Lecture Notes in Mathematics 962, Springer, Berlin (1982), 167-174. | MR 0682954 | Zbl 0498.18003

Pareigis B. Categories and Functors, Academic Press, London, 1970. | MR 0265428 | Zbl 0211.32402

Street R.; Walters R. Yoneda structures on 2-categories, J. Algebra 50 (1978), 350-379. (1978) | MR 0463261 | Zbl 0401.18004