Fiore, TM, Gambino, N orcid.org/0000-0002-4257-3590 and Kock, J (2011) Monads in double categories. Journal of Pure and Applied Algebra, 215 (6). pp. 1174-1197. ISSN 0022-4049
Abstract
We extend the basic concepts of Street’s formal theory of monads from the setting of 2-categories to that of double categories. In particular, we introduce the double category of monads in a double category and define what it means for a double category to admit the construction of free monads. Our main theorem shows that, under some mild conditions, a double category that is a framed bicategory admits the construction of free monads if its horizontal 2-category does. We apply this result to obtain double adjunctions which extend the adjunction between graphs and categories and the adjunction between polynomial endofunctors and polynomial monads.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2010, Elsevier. This is an author produced version of a paper published in Journal of Pure and Applied Algebra. Uploaded with permission from the publisher. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 13 May 2019 10:41 |
Last Modified: | 22 May 2019 14:23 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jpaa.2010.08.003 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:113168 |