Martin, P and Mazorchuk, V (2018) Fiat categorification of the symmetric inverse semigroup ISn and the semigroup Fn*. Semigroup Forum, 96 (1). pp. 142-159. ISSN 0037-1912
Abstract
Starting from the symmetric group Sn, we construct two fiat 2-categories. One of them can be viewed as the fiat “extension” of the natural 2-category associated with the symmetric inverse semigroup (considered as an ordered semigroup with respect to the natural order). This 2-category provides a fiat categorification for the integral semigroup algebra of the symmetric inverse semigroup. The other 2-category can be viewed as the fiat “extension” of the 2-category associated with the maximal factorizable subsemigroup of the dual symmetric inverse semigroup (again, considered as an ordered semigroup with respect to the natural order). This 2-category provides a fiat categorification for the integral semigroup algebra of the maximal factorizable subsemigroup of the dual symmetric inverse semigroup.
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Copyright, Publisher and Additional Information: | © 2017, The Author(s). This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ | ||||||
Keywords: | Categorification; 2-category; Symmetric inverse semigroup; Dual symmetric inverse semigroup | ||||||
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) | ||||||
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Depositing User: | Symplectic Publications | ||||||
Date Deposited: | 02 May 2017 10:08 | ||||||
Last Modified: | 19 Mar 2018 16:52 | ||||||
Status: | Published | ||||||
Publisher: | Springer Verlag | ||||||
Identification Number: | https://doi.org/10.1007/s00233-017-9866-5 |