Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
  • Home
Article
  • Cited by 2

  • Access

Note on monoidal monads

  • B. J. Day (a1)

Abstract

The representation theory of categories is used to embed each promonoidal monad in a monoidal biclosed monad. The existence of a promonoidal structure on the ordinary Eilenberg- Moore category generated by a promonoidal monad is examined. Several results by previous authors (notably A. Kock and F. E. J. Linton) are reproved and extended.

    •

      • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Note on monoidal monads
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Note on monoidal monads
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Note on monoidal monads
      Available formats
      ×

Copyright

COPYRIGHT: © Australian Mathematical Society 1977

References

Hide All
Bénabou, J. (1967), ‘Introduction to bicategories’, Reports of the Midwest Category Seminar I (Springer Lecture Notes, Vol. 47), 1–77.
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.
Day, B. J. (1970a), ‘On closed categories of functors’, Reports of the Midwest Category Seminar IV (Springer Lecture Notes, Vol. 137), 1–38.
Day, B. J. (1970b), ‘Construction of biclosed categories’, Ph.D. Thesis, University of New South Wales.
Day, B. J. (1973), ‘Note on monoidal localisation’, Bull. Austral. Math. Soc. 8, 1–16.
Day, B. J. (1974a), ‘On closed categories of functors II’, Category Seminar, Sydney 1972/73 (Springer Lecture Notes, Vol. 420), 20–53.
Day, B. J. (1974b), ‘An embedding theorem for closed categories’, Category Seminar, Sydney 1972/73 (Springer Lecture Notes, Vol. 420), 55–64.
Dubuc, E. (1970), Kan extensions in enriched category theory (Springer Lecture Notes, Vol. 145).
Eilenberg, S. and Kelly, G. M. (1966), ‘Closed categories’, Proc. Conference on Categorical Algebra, La Jolla, 1965 (Springer-Verlag, 1966), 421–562.
Kelly, G. M. (1974), ‘On clubs and doctrines’, Category Seminar, Sidney 1972/73 (Springer Lecture Notes, Vol. 420), 181–256.
Kock, A. (1970), ‘Monads on symmetric monoidal closed categories’, Archiv der Mathematik, Vol. XXI, 1–10.
Kock, A. (1971a), ‘Closed categories generated by commutative monads’, J. Austral. Math. Soc, 12, 405–424.
Kock, A. (1971b), ‘Bilinearity and cartesian closed monads’, Math. Scand., 29, 161–174.
Linton, F. E. J. (1969), ‘Coequalisers in categories of algebras’, Seminar on Triples and Categorical Homology Theory (Springer Lecture Notes, Vol. 80), 75–90.
Street, R. H. (1972), ‘The formal theory of monads’, J. of Pure and Applied Algebra, 2, 149–168.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.
  • Cited by 2

  • Access

Note on monoidal monads

  • B. J. Day (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed