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It's a little like abstract algebra, except more abstract and less algebraic.
It's a formalism used for making precise analogies between superficially unrelated mathematical theories.
Joseph Goguen has a nice paper A Categorical Manifesto [ucsd.edu], which explains clearly and convincingly why category theory is useful in computer science.
John Baez says (in this [ucr.edu] web page):
"If we try to generalize the heck out of
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