C.M.S. • Fredericton, NB • June 2010
Meditations on Arens Multiplication
   F.E.J. Linton • Wesleyan Univ. Math/CS Emeritus

1. Brief academic bio.
2. Arens’s phyla, presaging monoidal categories.
3. Arens’s phyla in a categorical time-line.
4. Dualization (*) and double dualization (**) in Arens’s phyla.
5. Arens’s principal ‡-construction (Arens multiplication): ** is monoidal.
6. Questions of symmetry/commutativity for **, and some answers, both positive ...
7. ... and, after some preparatory work on commutativity, ...
8. ... negative (Zalduendo, [1991]).
9. Questions, open problems, ...
10. ... and a parallel with Bohr compactification for Abelian groups.