Monoidal Categories for Use in Representation Theory

Abstract

We define a monoidal category based on the additive charge conservation idea used to classify constant Yang–Baxter solutions in [18]. We establish key structural properties of this category. We then use this to define a sequence of integer sequences. We find that this array unifies, in an algebraic setting, a number of known integer sequences that had previously been known to be connected only in a more combinatorial way. We do the same for the category of charge-conserving (CC) matrices. We investigate the algebraic structure of both linear categories.