Fiat categorification of the symmetric inverse semigroup IS_n and the semigroup F^*_n
Abstract
Starting from the symmetric group $S_n$, 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2016
 DOI:
 10.48550/arXiv.1605.03880
 arXiv:
 arXiv:1605.03880
 Bibcode:
 2016arXiv160503880M
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  Category Theory;
 Mathematics  Group Theory;
 Mathematics  Representation Theory
 EPrint:
 v2: minor revision