0. Introduction. The category of finite direct sums of standard (integrable highest weight) modules of a fixed positive integral level k for an affine Lie algebra ĝ is particularly important from the viewpoint of conformal field theory and related mathematics. Here we call this the category generated by the standard ĝ-modules of level k. A central theme is a braided tensor category structure (i...

The notion of centrality for crossed modules was introduced by Norrie in her thesis [7], in which she studied the category of crossed modules CM from an algebraic point of view, showing suitable generalizations of group theoretic concepts and results. Subsequently, Norrie’s approach was followed by Carrasco, Cegarra and R.-Grandjeán. In [5] they proved that CM is an algebraic category (i.e. the...