2012/05/24 by Samer Allouch, Allouch, Samer
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #math.CT
paper · pdf · doi:10.48550/arxiv.1205.5332
arxiv created 2012/05/24 · arxiv updated 2012/05/25
In the previous papers we found a direct method to confirm, for any square matrix, if it is associated to any categories or not. According to this method, the matrix 2 (all coefficients are 2) of a given order, admits associated categories. We determine in this paper the isomorphism classes of reduced categories that are associated with the matrix 2 of order 1, 2 and 3. More generally, we managed to give upper and lower bounds for the cardinal of the set of all reduced categories associated to the matrix 2 of a given order.