Dear Michael, This email is suggested by your announcement at ( http://www.math.mcgill.ca/makkai/) of papers on pasting and computads. First, I hope it is useful to direct people to an early paper with a definition of strict omega-categories, there called \infty-categories: (with P.J. HIGGINS), ``The equivalence of $\infty$-groupoids and crossed complexes'', {\em Cah. Top. G\'eom. Diff.} 22 (1981) 371-386. www.bangor.ac.uk/r.brown/pdffiles/x-comp.pdf The main emphasis of this paper is the equivalence in the title. Because crossed complexes C have a classifying space BC which can also be represented as a fibration over B\pi_1 C with fibre a topological abelian group (in fact the classifying space of a chain complex) this implies that the homotopy type of spaces represented by \infty-groupoids is limited. This observation suggested to Grothendieck in 1982 the need to move to weak \infty-categories (or groupoids) for dealing with matters of nonabelian cohomology, which for him was a long standing aim. It was not till I met him in 1986 that I convinced him that strict n-fold groupoids really did model all weak homotopy n-types, (Loday), at which he exclaimed `That is absolutely beautiful!' There is still work to do on the connections with nonabelian cohomology! And crossed complexes, though limited, are certainly useful for this, because of their close relation to chain complexes with operators. (for a survey on crossed complexes, see math.AT/0212274). Second, I would like to raise some general questions on multiple compositions and what is or should be the mathematics to deal with these. For 2-categories, this seems to be pasting schemes. However the thrust of my work since the 1970s has been to Higher Homotopy van Kampen theorems, (HHvKTs) based on the question of the possible use of groupoids in higher homotopy theory, given their success in 1-dimensional homotopy theory. The key aim was to use cubical methods, because these gave a convenient `algebraic inverse to subdivision', through the use of multiple compositions, modelling steps in the proof of the usual vKT for groupoids. Such HHvKTs were proved with Philip Higgins in dimension 2 in 1978, in all dimensions (for crossed complexes) in 1981, and with Jean-Louis Loday in 1987 (for cat^n groups and so crossed n-cubes of group). All these theorems have algebraic implications for homotopy types which seem unobtainable by other means. The theorems with PJH use directly `algebraic inverse to subdivision', while the proof with Loday uses some sophisticated algebraic topology and simplicial methods (Waldhausen, Zisman, Puppe and some new results). The work obtains to a limited extent a vision of Grothendieck of what he termed `integration of homotopy types'; there are strong connectivity assumptions so the theorems do not allow calculation of everything, e.g. homotopy groups of spheres, and so some have said `the theory has not fullfilled its promise' (report on a failed research proposal). On the other hand, the theory does come within the scope of `higher dimensional nonabelian methods for local-to-global problems', and the new explicit calculations enabled and relations with combinatorial group theory (e.g. the nonabelian tensor product of groups, bibiliography now of 90 items, http://www.bangor.ac.uk/~mas010/nonabtens.html) are pointers to its success. Possibly relevant to this is that I have never been able to write down a proof of even the 2-dimensional HHvKT using 2-groupoids; and it would not have been, or at least was not, even conjectured in those terms. My preference is for algebraic models of homotopy types which lead to some explicit algebraic computations (hence the HHvKTs), to new theorems, and new relations with other areas. My overall questions are therefore: (i) to what extent can and should cubical methods be used in weak category theory? (ii) is there some operadic or other method from current ideas on higher category theory which allows the use of `algebraic inverses to subdivision' in all dimensions? (iii) to what extent are these operadic methods generally useful in higher dimensional nonabelian methods for local-to-global problems? (I first heard of the term local-to-global problems from Dick Swan, when we worked on his lecture notes on the Theory of Sheaves, Oxford, 1958.) Of course subdivision allows the passage from global to local. The problem is the converse, a key problem in maths and science (even biology and engineering!). Anything which helps in this seems to me a Good Thing! Greetings and Good Luck, Ronnie Brown