文档介绍：An Introduction to Category Theory
Gorjan Alagic
University of Connecticut
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March 2004
Abstract
Category Theory initially arose in an algebraic topology paper by Samuel Eilenberg
and Saunders MacLane[1]. Very informally, it can be said that the ideas of Category
Theory stem from the general observation that a lot of things we do and study in
all levels and fields of mathematics are structurally very similar. In an attempt to
classify some of those similarities between groups and topological spaces, Eilenberg
and MacLane stumbled upon the beginnings of Category Theory[2]. Since then, it
has developed into an interesting field of its own, with countless pure and practical
applications ranging puter Science to Quantum Field Theory. Due to the
above informal notion, namely that Category Theory concerns itself with classifying
and studying the structure of mathematical objects, many consider it to be a subfield
of Algebra.
We will define the basic notions of the field, such as categories, functors, natural
transformations, and adjoints.
1 Introduction
These notes are intended to serve two purposes. First, they will serve as the background for
an introductory talk on the subject at the University of Connecticut. The goal of the talk
is to prepare graduate students for the occasional category theoretic concept that they may
run