Cheng, E. and Gurski, M.N. (2014) Iterated icons. Theory and Applications of Categories, 29 (32). pp. 929-977. ISSN 1201-561X
Abstract
We study the totality of categories weakly enriched in a monoidal bicategory using a notion of enriched icon as 2-cells. We show that when the monoidal bicategory in question is symmetric then this process can be iterated. We show that starting from the symmetric monoidal bicategory Cat and performing the construction twice yields a convenient symmetric monoidal bicategory of partially strict tricategories. We show that restricting to the doubly degenerate ones immediately gives the correct bicategory of `2-tuply monoidal categories' missing from our earlier studies of the Periodic Table. We propose a generalisation to all $k$-tuply monoidal $n$-categories.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Editors of Theory and Applications of Categories. |
Keywords: | Symmetric monoidal bicategory; icon; enriched category |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 13 May 2016 13:07 |
Last Modified: | 19 May 2016 10:50 |
Published Version: | http://www.tac.mta.ca/tac/volumes/29/32/29-32abs.h... |
Status: | Published |
Publisher: | Mount Allison University |
Refereed: | Yes |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:98613 |