{"paper":{"title":"Sandwich semigroups in locally small categories I: Foundations","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 {\\DJ}ur{\\dj}ev, James East, Jintana Sanwong, Kritsada Sangkhanan, Preeyanuch Honyam, Worachead Sommanee","submitted_at":"2017-10-05T06:09:31Z","abstract_excerpt":"Fix (not necessarily distinct) objects $i$ and $j$ of a locally small category $S$, and write $S_{ij}$ for the set of all morphisms $i\\to j$. Fix a morphism $a\\in S_{ji}$, and define an operation $\\star_a$ on $S_{ij}$ by $x\\star_ay=xay$ for all $x,y\\in S_{ij}$. Then $(S_{ij},\\star_a)$ is a semigroup, known as a sandwich semigroup, and denoted by $S_{ij}^a$. This article develops a general theory of sandwich semigroups in locally small categories. We begin with structural issues such as regularity, Green's relations and stability, focusing on the relationships between these properties on $S_{ij"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01890","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"}