2-category algebras: A student at Bangor, Ghaffar Mosa, did a thesis in: Higher dimensional algebroids and crossed complexes (1987). The aim was to define \omega-algebroids (following Brown-Higgins definition of \omega-groupoids) and to prove these equivalent to crossed complexes (in the context of algebroids), analogously to the Brown-Higgins equivalence between \omega-groupoids and crossed complexes of groupoids. (The former are essentially cubical.) A lot of information was found, some of which was a basis for the thesis of Al-Agl (Aspects of multiple categories, 1989), which has been subsumed in the paper of Al-Agl and Steiner in the Proc LMS. In effect, the equivalence is known up to dimension 3, for the case originally mooted, although there is presumably a version in the context of the Al-Agl/Steiner paper. An equivalence between crossed complexes of algebroids and globular infinity categories has been proved by Andy Tonks at Bangor. The point of the relation with crossed complexes is that these are part of the tradition in homological algebra from Rinehart, Frohlich, Lue, in which the notion of "chains of syzygies" starts with a resolution of an algebra in a general sense ("varieties of algebras"), leading initially to a crossed module in the appropriate context, rather than a module. In order to carry out the analogous work to that done for crossed complexes of groupoids work, it is also desirable to have a tensor product of such crossed complexes of algebras, as for the groupoid case. This was part of the aim of obtaining an equivalence between crossed complexes of algebroids and \omega-algebroids. However, even this equivalence would leave many questions open, since, as said above, crossed complexes are defined for "varieties of algebras", so one really wants a tensor product in this setting. Ronnie Brown +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++