Gambino, N orcid.org/0000-0002-4257-3590, Fiore, TM and Kock, J (2012) Double adjunctions and free monads. Cahiers de Topologie et Géométrie Differentielles Catégoriques, LIII (4). pp. 242-307. ISSN 1245-530X
Abstract
We characterize double adjunctions in terms of presheaves and universal squares, and then apply these characterizations to free monads and Eilenberg--Moore objects in double categories. We improve upon our earlier result in "Monads in Double Categories", JPAA 215:6, pages 1174-1197, 2011, to conclude: if a double category with cofolding admits the construction of free monads in its horizontal 2-category, then it also admits the construction of free monads as a double category. We also prove that a double category admits Eilenberg--Moore objects if and only if a certain parameterized presheaf is representable. Along the way, we develop parameterized presheaves on double categories and prove a double-categorical Yoneda Lemma.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2012, Author(s). This is an author produced version of a paper published in Cahiers de Topologie et Géométrie Differentielles Catégoriques. Uploaded in accordance with the publisher's self-archiving policy. |
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: | 08 Sep 2017 11:17 |
Last Modified: | 06 Feb 2018 13:53 |
Status: | Published |
Publisher: | Theory and Applications of Categories |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:113169 |