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They are the quiver-theoretic version of skew braces, an increasingly studied structure lying in the intersection of group and ring theory.\n  In this paper, we define ideals and quotients for quiver skew braces, with respect to two notions of morphisms. Following the track of a previous work of ours (2025), we define a classical semidirect product \\`a la Brown, and a categorical semidirect product \\`a la Bourn and Janelidze, for the category of quiver skew braces.\n  It i","authors_text":"Davide Ferri","cross_cats":["math.GR","math.QA"],"headline":"Quiver skew braces cannot be decomposed into a group of loops and vertices like connected groupoids can.","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.RT","submitted_at":"2026-05-12T10:16:51Z","title":"On quiver skew braces, their ideals and products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.11903","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-13T04:32:51.148221Z","id":"481780a5-8192-4021-b1f4-d69799e6708d","model_set":{"reader":"grok-4.3"},"one_line_summary":"Quiver skew braces lack the group-of-loops-plus-vertices decomposition that connected groupoids possess, and the paper equips them with ideals and two semidirect products.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Quiver skew braces cannot be decomposed into a group of loops and vertices like connected groupoids can.","strongest_claim":"It is known that connected groupoids can be expressed as the datum of a group of loops and a set of vertices. 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