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arXiv · 1605.03880

Fiat categorification of the symmetric inverse semigroup IS_n and the semigroup F^*_n

Paul Martin·Volodymyr Mazorchuk
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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.

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Paul Martin, Volodymyr Mazorchuk. 2017-03-27. Fiat categorification of the symmetric inverse semigroup IS_n and the semigroup F^*_n. https://arxiv.org/abs/1605.03880

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