We take another look at the Chu construction and show how to simplify it by looking at it as a module category in a trivial Chu category. This simplifies the construction substantially, especially in the case of a non-symmetric biclosed monoidal category. We also show that if the original category is accessible, then for any of a large class of ``polynomial-like'' functors, the category of coalgebras has cofree objects.
Keywords: Chu category, bimodules, cofree coalgebras.
AMS Classification (1991): 18D15.
Theory and Applications of Categories, Vol. 2, 1996, No. 2, pp 17-35.
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