{"paper":{"title":"Fiat categorification of the symmetric inverse semigroup IS_n and the semigroup F^*_n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.GR","math.RT"],"primary_cat":"math.RA","authors_text":"Paul Martin, Volodymyr Mazorchuk","submitted_at":"2016-05-12T16:22:57Z","abstract_excerpt":"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 o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03880","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}