The responses turned up some interesting and useful material on the web, which I'm still digesting. Notably [1] [2].
There's something in the introduction of [2] that I think will help me get a handle on this:
[[
... objects are not collections of "elements," and morphisms do not need to be functions between sets (thus morphisms cannot be applied to "elements" but only composed with other morphisms). Any immediate access to the internal structure of objects is prevented: all properties of objects must be specified by properties of morphisms ...
]]
My earlier supposition was that an "object" was roughly in correspondence with a member of a set, but I'm coming to perceive that "object" corresponds more with the notion of a set or collection of some (unspecified) things.
#g --
[1] http://www.cs.toronto.edu/~sme/presentations/cat101.pdf
[2] http://www.di.ens.fr/users/longo/download.html which has a link to content of the (apparently) out-of-print book: [[ CATEGORIES TYPES AND STRUCTURES An Introduction to Category Theory for the working computer scientist Andrea Asperti Giuseppe Longo FOUNDATIONS OF COMPUTING SERIES, M.I.T. PRESS, 1991 ]]
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------------ Graham Klyne [EMAIL PROTECTED]
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