Xref: utzoo sci.math:12067 comp.theory:967 Path: utzoo!attcan!utgpu!news-server.csri.toronto.edu!mailrus!tut.cis.ohio-state.edu!cs.utexas.edu!usc!sdd.hp.com!decwrl!fernwood!portal!cup.portal.com!Victoria_Beth_Berdon From: Victoria_Beth_Berdon@cup.portal.com Newsgroups: sci.math,comp.theory Subject: Re: Intro Category Theory? Message-ID: <32952@cup.portal.com> Date: 18 Aug 90 08:37:29 GMT References: Organization: The Portal System (TM) Lines: 83 August 17, 1990 I, too, am starting to study category theory. But I was afraid to post anything on the net. So you have done it for me, just as I would have wanted. I found several good ('tho still dense, but less so) references to recommend, as well as several articles: Books: *The Logical Foundations of Mathematics*, William S. Hatcher, Pergamon Press, 1982. Chapter 8:Categorical Algebra. (A good overview) *Topoi: The Categorial Analysis of Logic* , Studies in Logic and the Foundations of Mathematics, by R. Goldblatt, North-Holland, 1984. Particularly the first three chapters. *A Course in Homological Algebra*, P.J. Hilton and U. Stammbach, Springer- Verlag, 1970. Chapter II. (This is quite dense.) *Introduction to Higher Order Categorical Logic*, J. Lambek and P.J. Scott, Cambridge University Press, 1986. I've been told that F. W. Lawvere is one of the early developers, too. Solomon Feferman is mentioned much. Saunders MacLane (one of the founders of Cat. Theory, 1945) is probably the best place to start. Try some articles. Articles: *Categorical Algebra and Set Theorectic Foundations*, Saunders MacLane. (Sorry, I have no further reference...just an old copy) J.L. Bell, from the London School of Economics, is writing furiously in the topic now. See journals such as Synthese and The British Journal for the Philosophy of Science. *Category Theory and the Foundations of Mathematics*, J.L. Bell, Brit. J.Phil. Sci. 32 (1981), 349-358. *From Absolute to Local Mathematics*, J.L. Bell, Synthese 69 (1986) 409-426. *Categories, Toposes and Sets*, J.L. Bell, Synthese 51 (1982) 293-337. For some general flavor: *Working Foundations*, Solomon Feferman, Synthese 62 (1985) 229-254. For an interesting application: *Infinitesimals*, J.L. Bell, Synthese 75 (1988) 285-315. *Category Theory and Concrete Universals*, David P. Ellerman, Erkenntnis 28, 409-429, May 1988. AVOID Michal Tempczyk's *Categories and Elementary Particle Physics*, Dialectics and Humanism 9, 119-130, Winter 1982. He does not understand even the most elementary notions, such as initial objects and terminal objects, or morphism. Nice idea he had (to model E.P.P. with Category Theory...after all, they have had such good results with algebra. But he hasn't managed it.) You might try looking in the Philosopher's Index (in the reference section of the library) for further, and more recent references of a less technical nature than the usual math refs. That's where I got most of these article references. Enough. What are you doing with Category Theory? Are you a math student? Other? Where? I am a philosophy grad student writing a master's thesis in foundations of, and phil. of mathematics. Category theory is all that my advisor is interested in. Possible topics under consideration: the internal logic of topoi (categories of sets that vary) -- it seems to be of an intuitionistic flavor, in that the law of excluded middle fails. Perhaps a compare and contrast of well-known math reinterpretted in category-theoretic language? (see the Infinitesimals paper by Bell for an example) I'm in San Francisco, and will be away 8/21-9/4, but would very much like to correspond with someone on category theory, itself, or its implications. I hope to hear from you! Good luck, and don't be discouraged. Two minds work (at least) three times better!