Summary: Theory and Applications of Categories, Vol. 14, No. 8, 2005, pp. 157--199.
INTRODUCTION TO COALGEBRA
R ’ I AD ’
Abstract. A survey of parts of General Coalgebra is presented with applications to
the theory of systems. Stress is laid on terminal coalgebras and coinduction as well as
iterative algebras and iterative theories.
1. Preface: Is this Really an Introduction to Coalgebra?
For my series of lectures on coalgebra on the preconference to CTCS 2002 I prepared a
short text called ``Introduction to Coalgebra'' that was intended to cover the material
of the series. I was not worried about the the choice of topics: they were given by the
intentions of the course. Two years later the Program Chair Rick Blute suggested that I
could publish the text in the proceedings---and after I agreed, I found myself in a fix: what
topics to choose? If I add to the existing text the minimum of material that would indeed
constitute a general introduction to coalgebra, the text would grow immensely. Besides,
excellent introductions exist already, see e.g. [R1], [G], [JR]. I decided for a minimalistic
approach: in the following sections I try and present an introduction to the parts of
coalgebra which are those ``dearest to my heart'', and to which I have also contributed.
Thus, a substantial part of coalgebra topics is not mentioned at all; I hope the reader will