The course notes ( ps.gz, ps) are available in a revised version from October 2001.

**Sketch of the 5 Lectures**:

**Recommended Literature** (updated May 2002):

I plan to make the lecture self contained, so it will not be necessary to read any of the following. If you want to prepare a bit nevertheless read on modal logic and on category theory (see below). The remaining references are for the curious ...

B. Jacobs and J.J.M.M. Rutten,

Probably the best for a first introduction.

J.J.M.M. Rutten,

This paper contains a thorough study of universal coalgebra and contains background material for further studies.

Another more recent reference for universal coalgebra are the lecture
notes

H. Peter Gumm, *Elements of the general theory of coalgebras.* LUATCS'99,
Rand Afrikaans University, Johannesburg, South Africa, 1999.

W. Wechler,

P. Blackburn, M. de Rijke, Y. Venema,

My ESSLLI-lecture will present what is necessary to know about modal logic in order to understand the relationship to coalgebras. But to really appreciate this relationship (which has only been discovered during the last few years) some additional background on modal logic will be useful: For this read chapters 1.1 - 1.3, 2.1 - 2.3, and note theorem 2.65.

J. Barwise, L. Moss,

A very readable and exciting book on paradoxa, non-well founded set theory, coalgebras, and modal logic.

Lawvere, Schanuel, *Conceptual Mathematics*, Cambridge University
Press, 1996.

This book teaches to think categorically and avoids technicalities or
advanced examples. Take a look!

S. Mac Lane, *Categories for the Working Mathematician*, Springer
1971.

The classical reference.

J. Adamek, H. Herrlich, G. Strecker, * Abstract and Concrete
Categories *, John Wiley and Sons, 1990.

Presents a lot of material not available in Mac Lane's book.

A. Asperti,
G. Longo. * Categories, Types and Structures*, MIT Press,
1991.

For those who are interested in the relationship between
category theory and type theory. Electronically available.

M. Barr, C. Wells, * Category Theory for Computing Science*,
Prentice Hall, 1990.

A very readable introduction with many
examples familiar to computer scientists. A shorter introduction is
electronically available as the lecture notes of their ESSLLI'99
course.

F. Borceux. *Handbook of Categorial Algebra.* Cambridge University
Press, 1994.

Perhaps not the best starter but most valuable for
learning category theory seriously.

B. Pierce, * Basic Category Theory for Computer Scientist*, MIT
Press, 1991.

A small book but still containing all the definitions
mentioned above.

R.F.C. Walters, * Categories and Computer Science*, MIT Press,
1991.

An undergraduate text emphasising objects as data types and
arrows as programs.

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.

Chris Hillman: *A
Categorical Primer.* August 2001.

Tom Leinster: *
Category Theory.*

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

Jaap van Oosten: *
Basic Category Theory.*

D. Turi: *Category
Theory Lecture Notes.* LFCS, Univeristy of Edinburgh, 2001.

Alexander Kurz Last modified: Wed May 15 10:49:01 CEST 2002