Category Theory vs. General Systems Theory

Posted on January 28, 2008 by Tommy McGuire
Labels: math
After moving to northern Alabama this winter (and seeing the job openings in Huntsville), I took an Systems Engineering Overview course through the University of Alabama at Huntsville Continuing Education. One of the things I learned is that I am not particularly interested in becoming a Systems Engineer (I am a technical guy and a computer scientist; project management is not fascinating). The other is that the definition of a system according to General Systems Theory (the nominal, theoretical roots of systems engineering),
"A system is here defined as a set of objects together with relationships between the objects and between their attributes related to each other and to their environment so as to form a whole."
is almost the same as that of a category in mathematical category
theory,
a collection of mathematical entities and the relationships which exist between those entities

The difference is that in category theory the objects have no internal attributes or structure and that if an environment is necessary, it is represented as one or more additional objects.

If anyone has a tame professor of mathematics handy, I am sure there are several dissertations in this observation. (I cannot help much; I am still waiting for "Category Theory for the Slobbering Moron". But give me a footnote if you can.)
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