I would also point to the papers by Andrée and Charles Ehresmann: Multiple functors. II. The monoidal closed category of multiple categories. Cahiers Topologie Géom. Différentielle 19 (1978), no. 3, 295–333. Multiple functors. III. The Cartesian closed category ${\rm Cat}_{n}$. Cahiers Topologie Géom. Différentielle 19 (1978), no. 4, 387–443. ==Ross On 08/12/2010, at 1:13 AM, Ronnie Brown wrote:
I am not sure why there is the restriction to having 2-categories as edge arrows. They could be double categories, perhaps. Would this then be any more general than a 4-fold category?
A definition of n-fold category is given in
34. (with P.J. HIGGINS), ``The equivalence of $\infty$-groupoids and crossed complexes'', {\em Cah. Top. G\'eom. Diff.} 22 (1981) 371-386.
and this also contains a definition of what was later called a globular set, giving a notion of what we now call a strict globular n-category, though the emphasis in the paper is on the groupoid case.
Ronnie
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