Thanks: (was Question about categories)
Graham Klyne
GK at ninebynine.org
Mon Sep 22 14:28:48 EDT 2003
Thanks to everyone who responded to my question about category theory.
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
GK at NineByNine.org
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