ONT Reflections On Categories
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Some years ago, when I was taking a course on "applications of lambda calculus"
that made use of the then-evolving connections between combinator logic, models
of lambda calculus, and cartesian closed categories, I started to work on the
idea of computing in categories, by which I meant chasing arrows by computer.
The fact that I had just developed a suite of programs for doing matching in
graphs led me to view this project in terms of the underlying graph-theoretic
data structures that I would use to represent categories, morphisms, functors,
natural transformations, and so on. I never got to finish this work, but the
graph-theoretic pictures that I developed along the way are ones that I still
use to think about the skeletal structure ("bare bones") of category theory.
Now that the ontology project is contemplating the use of category theory
as a medium for its work, I thought that this way of viewing the subject
might be of service in elucidating a sample of its most basic notions.
So I will dedicate this line of exposition to doing that.
Jon Awbrey
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