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

      Richard Arens, Operations induced in function classes. Monatsh. für Math. 55 (1951), 1-19 (submitted April 1950).

  Shows that ** (double dualization) in linear spaces, or in Banach spaces, is a monoidal functor, but not a symmetric one ...

... a good decade before monoidal categories or their relatives (closed categories, multilinear categories) were consciously recognized as such.

  Arens’s formalization — of phyla or genetically closed systems — foreshadowed symmetric closed monoidal categories (in the E-K terminology), or perhaps symmetric closed monoidal multilinear ones.