文档介绍：Category Theory
Steve Awodey
Carnegie Mellon University
in memoriam
Saunders Mac Lane
Preface
Why write a new textbook on Category Theory, when we already have Mac
Lane’s Categories for the Working Mathematician? Simply put: because
Mac Lane’s book is for the working (and aspiring) mathematician. What
is needed now, after 30 years of spreading into various other disciplines and
places in the curriculum, is a book for everyone else.
This book has grown from my courses on Category Theory at Carnegie
Mellon University over the last ten years. In that time, I have given numer-
ous lecture courses and advanced seminars to undergraduate and graduate
students puter Science, Mathematics, and Logic. The lecture course
based on the material in this book consists of two, 90-minute lectures a week
for 15 weeks. The germ of these lectures was my own graduate student notes
from a course on Category Theory given by Mac Lane at the University of
Chicago. In teaching my own course, I soon discovered that the mixed group
of students at Carnegie Mellon had very different needs than the Mathemat-
ics graduate students at Chicago, and my search for a suitable textbook to
meet these needs revealed a serious gap in the literature. My lecture notes
evolved over time to fill this gap, supplementing and eventually replacing the
various texts I tried using.
The students in my courses often have little background in Mathematics
beyond a course in Discrete Math and some Calculus or Linear Algebra or a
course or two in Logic. heless, eventually, as researchers puter
Science or Logic, many will need to be familiar with the basic notions of
Category Theory, without the benefit of much further mathematical train-
ing. The Mathematics undergraduates are in a similar boat: mathematically
talented, motivated to learn the subject by its evident relevance to their
further studies, yet unable to follow Mac Lane because they still lack the
mathematical prerequisites. Most o