{"paper":{"title":"Sandwich semigroups in locally small categories II: Transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RA"],"primary_cat":"math.GR","authors_text":"Igor Dolinka, Ivana {\\DH}ur{\\dj}ev, James East, Jintana Sanwong, Kritsada Sangkhanan, Preeyanuch Honyam, Worachead Sommanee","submitted_at":"2017-10-05T06:16:29Z","abstract_excerpt":"Fix sets $X$ and $Y$, and write $\\mathcal{PT}_{XY}$ for the set of all partial functions $X\\to Y$. Fix a partial function $a:Y\\to X$, and define the operation $\\star_a$ on $\\mathcal{PT}_{XY}$ by $f\\star_ag=fag$ for $f,g\\in\\mathcal{PT}_{XY}$. The sandwich semigroup $(\\mathcal{PT}_{XY},\\star_a)$ is denoted $\\mathcal{PT}_{XY}^a$. We apply general results from Part I to thoroughly describe the structural and combinatorial properties of $\\mathcal{PT}_{XY}^a$, as well as its regular and idempotent-generated subsemigroups, Reg$(\\mathcal{PT}_{XY}^a)$ and $\\mathbb E(\\mathcal{PT}_{XY}^a)$. After describ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01891","kind":"arxiv","version":3},"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"}