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From: baxter@zola.ICS.UCI.EDU (Ira Baxter)
Newsgroups: comp.theory
Subject: Re: Intro Category Theory?
Message-ID: <9008161733.aa29977@PARIS.ICS.UCI.EDU>
Date: 17 Aug 90 00:36:44 GMT
References: <VICTOR.90Aug16142815@vivaldi.itg.ti.com>
Lines: 91

In comp.theory you write:

>I have been starting to get into Category Theory, but find some of the books
>rather dense.  Are there any good intro books out there?  My backround is CS
>with some moderate mathematics (more enthusiasm than ability, I fear!).  It
>doesn't matter to me whether the texts are oriented towards math or CS.

I recently went through this myself, with only moderate success.
I feel like I know have "survival category theory" understanding.
Call me "the reluctant mathematician".
Here are some references and my remarks on them:

@book(Arbib75a,
  author     = "Michael A. Arbib and Ernest G. Manes",
  title      = "{Arrows, Structures, and Functors: The Categorical Imperative}",
  publisher  = "Academic Press",
  address    = "New York",
  year       = 1975,
  note       = "",
  annotation = {An attempt to simplify the presentation of category
theory to make it more widely accessible.  Unfortunately, the authors
do not succeed, as they fail to make it clear to the poor reader when
the discussion is about specific instances of categories, and when
the discussion is about categories in general, and the switching back
and forth is very rapid.  Such a consequence is not a surprise;
it must be extremely difficult for a CT to come "down out of the clouds".
One must give the authors credit for a
heroic attempt at a nearly impossible task anyway.
The determined reader can make some headway; this book is useful
as one of several references simultaneously necessary to really
learn category theory. \cite{Goldblatt84a} is much better.
The book shows some application of category theory to finite state automata.}
)

@book(Rydeheard:computational-category-theory,
  author     = "D. E. Rydeheard and R. M. Burstall",
  title      = "{Computational Category Theory}",
  publisher  = "Prentice-Hall",
  address    = "New York",
  year       = 1988,
  note       = "ISBN 0-13-162736-8",
  annotation = {Contains an introduction to category theory with
		emphasis on defining computations in categories.  The
		language in  which the computations are defined is
		ML, but it appears that any functional language would
		do (I coded some of the examples in Common Lisp).
		Not really valuable to learn category theory;
		\cite{Goldblatt84a} is better, but is a good way to
		solidify one's understanding of category theory by
		working with concrete, programmable examples.  I
		particularly liked the computation of pushouts.}
)

@techreport(Srinivas90a:category-theory-summary,
  author     = "Yellamraju V. Srinivas",
  title      = "Category Theory: {D}efinitions and Examples",
  institution= "Dept. of ICS, University of California, Irvine",
  number     = "90-14",
  month      = feb,
  year       = 1990
)

@book(Goldblatt84a,
  author     = "R. Goldblatt",
  title      = "{Topoi: The Categorial Analysis of Logic}",
  publisher  = "North-Holland",
  address    = "New York",
  year       = 1984,
  annotation = {This book defines Logic using Category
Theory as a basis.  The real value of this book is that its first
5 chapters are the most readable introduction to category theory that
this reader has encountered.}
)

@book(Pitt85a:category-theory-and-computer-programming-workshop,
  editor     = "David Pitt and Samson Abramsky and Axel Poigne and David Rydeheard",
  title  = "{Category Theory and Computer Programming}",
  publisher  = "Springer-Verlag, New York",
  year       = 1985,
  note       = "Lecture Notes in Computer Science 240",
  annotation = {Workshop proceedings.  Contains category theory
tutorial focused on computer science topics so the example domains are
easier for us poor computer scientists to comprehend.  Also contains
a number of research papers on category theory applied to semantics
of programming languages, program specification, categorical logic and
categorical programming.}
)

Good luck.
--
Ira Baxter