Gambino, N orcid.org/0000-0002-4257-3590 and Lobbia, G orcid.org/0000-0002-2732-0317 (2021) On the formal theory of pseudomonads and pseudodistributive laws. Theory and Applications of Categories, 37 (2). pp. 14-56. ISSN 1201-561X
Abstract
We contribute to the formal theory of pseudomonads, i.e. the analogue for pseudomonads of the formal theory of monads. In particular, we solve a problem posed by Lack by proving that, for every Gray-category K, there is a Gray-category Psm(K) of pseudomonads, pseudomonad morphisms, pseudomonad transformations and pseudomonad modifications in K. We then establish a triequivalence between Psm(K) and the Gray-category of pseudomonads introduced by Marmolejo and give a simpler proof of the equivalence between pseudodistributive laws and liftings of pseudomonads to 2-categories of pseudoalgebras.
Metadata
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Copyright, Publisher and Additional Information: | © Nicola Gambino and Gabriele Lobbia, 2021. Permission to copy for private use granted. This is an author produced version of a paper published in Theory and Applications of Categories. Uploaded in accordance with the publisher's self-archiving policy. | ||||
Keywords: | pseudomonads, distributive laws, Gray-categories | ||||
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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) | ||||
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Depositing User: | Symplectic Publications | ||||
Date Deposited: | 27 Jan 2021 12:02 | ||||
Last Modified: | 27 Jun 2021 08:16 | ||||
Published Version: | http://www.tac.mta.ca/tac/index.html | ||||
Status: | Published | ||||
Publisher: | Mount Allison University |