A Thesis Proposal on Final Coalgebras

I present an overview of nal coalgebras together with a description of initial algebras, showing the analogies between the two. In particular , I show how initiality of algebras leads to the properties of deenition by recursion and proof by induction. I then show how nal coalgebras have the analogous properties of deenition by corecursion and proof by coinduction, motivating the latter by Peter Aczel's anti-foundation set theory. I present two of the current existence theorems for nal coal-gebras (the rst due to Michael Barr and the second to Peter Aczel and Nax Mendler). Finally, I present a list of some open questions/research projects that I intend to study for my dissertation.