A paper for people who fear categories.

A paper for people who fear categories.

[Noson Yanofsky]

Dear Esteemed Category Theorists,

I have written the following paper for the
few people in the world who dread/hate category theory.
(I have been told such people exist. Perhaps you know of
some.) The paper takes an idea of Lawvere and puts
it into a language of sets and functions. Many examples are
given to show how one scheme can describe numerous diverse
phenomena.
The paper should be readable by any undergraduate with a
discrete math course. No category theory is used in the paper
but the spirit of category theory is employed throughout.

Enjoy,
Noson Yanofsky
===============================

A Universal Approach to Self-Referential
Paradoxes, Incompleteness and Fixed Points

Abstract:
Following F. William Lawvere, we show that many
self-referential paradoxes, incompleteness theorems
and fixed point theorems fall out of the same
simple scheme. We demonstrate these similarities
by showing how this simple scheme encompasses the
semantic paradoxes, and how they arise as diagonal
arguments and fixed point theorems in logic,
computability theory, complexity theory and formal
language theory.


Available at:
http://xxx.lanl.gov/abs/math.LO/0305282