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
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.