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computerscience

Electronically Available Books and Other Sources (mainly Category Theory)


Books on Category Theory

nLab Not a book in the traditional sense, more like a wiki, containing much recent category theory not (easily) available elsewhere.

J. Adamek, H. Herrlich, G. Strecker: Abstract and Concrete Categories. John Wiley and Sons, 1990. Contains a lot of material not available in Mac Lane's book. Indispensable for me.

A. Asperti, G. Longo: Categories, Types and Structures. MIT Press, 1991. Emphasises the relationship between category theory and type theory.

M. Barr, C. Wells: Toposes, Triples and Theories. Springer, 1983. A classic text.

M. Kelly: Basic Concepts of Enriched Category Theory. Cambridge University Press, 1982. TAC-reprint 2005.

D.E. Rydeheard, R.M. Burstall: Computational Category Theory. Prentice-Hall, 1988. (See also here)


Lecture Notes on Category Theory

M. Barr, C. Wells: Introduction to Category Theory. Lecture Notes of an ESSLLI'99 course.

G. Bergman: An Invitation to General Algebra and Universal Constructions. 1998. An introduction to category theory that carefully explains many (universal) constructions in algebra and neighbouring fields. I enjoyed it a lot.

M. Caccamo, J.M.E. Hyland, G. Winskel: Lecture Notes in Category Theory. BRICS Lecture Series, 2001.

M. Fokkinga: A Gentle Introduction to Category Theory - the calculational approach. University of Utrecht, 1992.

T. Leinster: Category Theory. This page contains an informal introduction to category theory and, for example, a nice explanation of the Yoneda Lemma.

J. van Oosten: Basic Category Theory.

H. Simmons: An introduction to Category theory in four easy movements.

D. Turi: Category Theory Lecture Notes. LFCS, Univeristy of Edinburgh, 2001. If I had the opportunity to teach a first course on category theory I might choose these as my notes.


Special Topics in Category Theory

Reprints in Theory and Applications of Categories.

Larry Moss: Non-wellfounded Set Theory.

Benabou: Distributors at Work. Course notes, 2000.

E. Cheng, A. Lauda: Higher-Dimensional Categories: an illustrated guide book. Draft, 2004.

T. Leinster: Higher Operads, Higher Categories. CUP, 2004.

Thomas Streicher: Category Theory and Categorical Logic. Course notes, 2004.

Thomas Streicher: Categorical Models of Constructive Logic. Course notes, 2003.

Thomas Streicher: Fibred Categories a la Benabou. Course notes, 1999, revised 2003.


Journals

Theory and Applications of Categories. Maintained by researchers and freely available, it is the main journal on category theory and its applications.

Logical Methods in Computer Science. Maintained by researchers and freely available (started in 2005), it may well become the leading journal in theoretical computer science. Some of the best recent categorical papers in computer science can be found here.


Historical Sources

NUMDAM Archive of ancient mathematics documents. Scanned copies of French journals and seminaires from 1810 until today. (With papers of, for example, Chevalley, Ehresmann, Eilenberg, Grothendieck, Moore)

Grothendieck Circle. Website with biographical information about and mathematical work of Alexander Grothendieck.

Related and Unrelated Areas

J. Barwise and S. Feferman: Model-Theoretic Logics. Springer 1985.

S.N. Burris and H.P. Sankappanavar: A Course in Universal Algebra. Springer, 1981. A classic text which is still a useful introduction.

J.-Y. Girard, Y. Lafont and P. Taylor: Proofs and Types. CUP, 1989. Long out of print but luckily available online.

R. Goldblatt: Mathematics of Modality. CSLI, 1993. Contains many of Goldblatt's groundbraking papers on modal logic.

A. Hatcher: Algebraic Topology. CUP, 2002. I find it a very readable introduction emphasising geometric intuition.

R. Sutton, A. Barto: Reinforcement Learning: An Introduction MIT Press, Cambridge, MA, 1998.

M. Felleisen, R. Findler, M. Flatt, S. Krishnamurthi: How To Design Programs MIT Press, Cambridge, MA, 2003.

More Mathematics

AMS Books Online (see also here)

University of Pennsylvania Library, The Online Books Page

Textbooks in Mathematics

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Author: Alexander Kurz, T: +44 (0) 116 252 5356.
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