Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-23T14:02:47.228Z Has data issue: false hasContentIssue false
  • English
  • Français

Promonoidal functor categories

Published online by Cambridge University Press:  09 April 2009

B. J. Day
B. J. Day
Affiliation:
Department of Pure Mathematics, University of Sydney, N.S.W. 2006, Australia.
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.

In this article a completion process for promonoidal categories is used to determine a sufficient condition for the existence of a promonoidal convolution structure on the category of functors between two promonoidal categories. This, in turn, leads to a partial closed structure on the 2-category of promonoidal categories, promonoidal functors, and promonoidal natural transformations.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 3 , May 1977 , pp. 312 - 328
Copyright
Copyright © Australian Mathematical Society 1977

References

Bénabou, J. (1967), ‘Introduction to bicategories’, Reports of the Midwest Category Seminar I (Springer Lecture Notes, Vol. 47), 1–77.Google Scholar
Borceux, F. and Kelly, G. M. (1975), ‘A notion of limit for enriched categories’, Bull. Austral. Math. Soc. 12, 49–72.CrossRefGoogle Scholar
Day, B. J. and Kelly, G. M. (1969), ‘Enriched functor categories’, Reports of the Midwest Category Seminar III (Springer Lecture Notes, Vol. 106), 178–191.CrossRefGoogle Scholar
Day, B. J. (1970a), ‘On closed categories of functors’, Reports of the Midwest Category Seminar IV (Springer Lecture Notes, Vol. 137), 1–38.Google Scholar
Day, B. J. (1970b), ‘Construction of biclosed categories’, Ph.D. thesis, University of New South Wales.Google Scholar
Day, B. J. (1973), ‘Note on monoidal localisation’, Bull. Austral. Math. Soc., 8, 1–16.Google Scholar
Day, B. J. (1974a), ‘On closed categories of functors II’, Category Seminar, Sydney 1972/73 (Springer Lecture Notes, Vol. 420), 20–53.CrossRefGoogle Scholar
Day, B. J. (1974b), ‘An embedding theorem for closed categories’, Category Seminar, Sydney 1972/73 (Springer Lecture Notes, Vol. 420), 55–64.Google Scholar
Day, B. J. (1977), ‘Note on monoidal monads’, J. Austral. Math. Soc. (Ser. A) 23, 292–311.CrossRefGoogle Scholar
Dubuc, E. (1970), Kan extensions in enriched category theory (Springer Lecture Notes, Vol. 145).CrossRefGoogle Scholar
Eilenberg, S. and Kelly, G. M. (1966), ‘Closed categories’, Proc. Conference on Categorical Algebra, La Jolla, 1965 (Springer-Verlag), 421–562.CrossRefGoogle Scholar
Kock, A. (1971), ‘Closed categories generated by commutative monads’, J. Austral. Math. Soc. 12, 405–424.Google Scholar
Lane, S. Mac (1971), Categories for the working mathematician (GTM5, Springer-Verlag, New York, Heidelberg, Berlin).Google Scholar
Street, R. H. (1976), ‘Limits indexed by category-valued 2-functors’; to appear in J. Pure and Applied Algebra, Vol. 10.Google Scholar