2013/04/25 by Katsuhiko Kuribayashi, Kuribayashi, Katsuhiko, Kentaro Matsuo +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.CO #math.CT
paper · pdf · doi:10.48550/arxiv.1304.6883
27 pages, Lemma 6.10 is revised adding a condition
openalex publication_date 2013/04/25 · arxiv created 2013/08/13 · arxiv updated 2013/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose the notion of association schemoids generalizing that of association schemes from small categorical points of view. In particular, a generalization of the Bose-Mesner algebra of an association scheme appears as a subalgebra in the category algebra of the underlying category of a schemoid. In this paper, the equivalence between the categories of grouopids and that of thin association schemoids is established. Moreover linear extensions of schemoids are considered. A general theory of the Baues-Wirsching cohomology deduces a classification theorem for such extensions of a schemoid. We also introduce two relevant categories of schemoids into which the categories of schemes due to Hanaki and due to French are embedded, respectively.