Abstract
Flows with respect to a functor F are introduced as a common generalization of the concepts of F-co-structured sinks and small F-co-structured sources. Appropriate factorization structures for functors are investigated and used to obtain several results that characterize coadjoint functors that have domains with various completeness conditions. When the functor in question is an identity functor, these results reduce to earlier results of Herrlich and Meyer for flows in a category. Functors of the type in question are shown to be nicely behaved with respect to composition. The dual notion of wolfs with respect to a functor is introduced, as is the concept of (co)limit with respect to a functor.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adámek, J., Herrlich, H. and Strecker, G. E.: Abstract and Concrete Categories, Wiley, New York, 1990.
Bousfield, A. K.: Construction of factorization systems in categories, J. Pure Appl. Algebra 9 (1976/77), 207–220.
Cassidy, C., Hébert, M. and Kelly, G. M.: Reflective subcategories, localizations, and factorization systems, J. Austral. Math. Soc. 38 (1985), 287–329. Ibid 41 (1986), 286.
Herrlich, H. and Meyer,W.: Factorization of flows and completeness of categories, Quaestiones Math. 17 (1994), 1–11.
Herrlich, H. and Strecker, G. E.: Semi-universal maps and universal initial completions, Pacific J. Math. 82 (1979), 405–528.
Hoffmann, R.-E.: Factorization of cones, Math. Nachr. 87 (1979), 221–238.
Kennison, J. F.: On limit preserving functors, Illinois J. Math. 12 (1968), 616–619.
Lambek, J.: Completions of Categories, Lecture Notes in Math. 24, Springer, 1966.
Street, R.: The family approach to total cocompleteness and toposes, Trans. Amer. Math. Soc. 284 (1984), 355–369.
Tholen, W.: Pro-categories and multiadjoint functors, Canad. J. Math. 36 (1984), 144–155.
Tholen,W. and Tozzi, A.: Completions of categories and initial completions, Cahiers Topologie Géom. Differentielle Catégoriques 30(2) (1989), 127–156.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Strecker, G.E. Flows With Respect to a Functor. Applied Categorical Structures 8, 559–578 (2000). https://doi.org/10.1023/A:1008654922010
Issue Date:
DOI: https://doi.org/10.1023/A:1008654922010