Abstract 3 Weber

In the third lecture we describe how one can generate inductive definition schema of the type sought for semi strict n-categories. One way in which Gray categories are strict, is that they have identity cells in each dimension which really act as strict identities with respect to all the other operations. There is a variant of the notion of Batanin higher operad describing structures whose algebras are higher categorical structures possessing strict units, and an analogous notion of weak n-category with strict units. Any n-dimensional strictly unital structure admits a definition by iterated enrichment, and in particular, one has a tensor product of weak n-categories with strict units such that enriching over this gives weak (n+1)-categories with strict units.

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