On the Lie transformation algebra of monoids in symmetric monoidal categories (Q396491)

Let \(K\) be a field. The main goal of this paper is to extend the theory of inner derivations for nonassociative algebras developed by \textit{R. D. Schafer} [Bull. Am. Math. Soc. 55, 769--776 (1949; Zbl 0033.34803)] to monoids over a \(K\)-linear symmetric monoidal category. Moreover, if \(A\) is an associative monoid, the author describes the Lie transformation algebra (Proposition 2.2) and inner derivations of \(A\) (Proposition 2.3). Finally, he shows (Proposition 2.5) that derivations preserve the nucleus of the monoid \(A\).