Graves, D (2022) Composing PROBs. Theory and Applications of Categories, 38 (26). 26. pp. 1050-1061. ISSN 1201-561X
Abstract
A PROB is a "product and braid" category. Such categories can be used to encode the structure borne by an object in a braided monoidal category. In this paper we provide PROBs whose categories of algebras in a braided monoidal category are equivalent to the categories of monoids and comonoids using the category associated to the braid crossed simplicial group of Fiedorowicz and Loday. We show that PROBs can be composed by generalizing the machinery introduced by Lack for PROPs. We use this to define a PROB for bimonoids in a braided monoidal category as a composite of the PROBs for monoids and comonoids.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Daniel Graves, 2022. Permission to copy for private use granted. This is an author produced version of an article, published in / accepted for publication in Theory and Applications of Categories. Uploaded with permission from the publisher. |
Keywords: | PROB, bimonoid, bialgebra, braided monoidal category, crossed simplicial group, distributive law |
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: | 01 Sep 2022 10:39 |
Last Modified: | 25 Jun 2023 23:05 |
Published Version: | http://www.tac.mta.ca/tac/volumes/38/26/38-26abs.h... |
Status: | Published |
Publisher: | Mount Allison University |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:190446 |