Classification des cat\'egories associ\'ees \`a la matrice des coefficients 2 d'ordre donn\'ee

Abstract

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.