In Search of Terminal Coalgebras
Posted by David Corfield
Tom Leinster has put up the slides for his joint talk – Terminal coalgebras via modules – with Apostolos Matzaris at PSSL 88.
It’s all about establishing the existence of, and constructing, terminal coalgebras in certain situations. I realise though looking through the slides that I never fully got on top of the flatness idea, and nLab is a little reluctant to help at the moment (except for flat module).
So perhaps someone could help me understand the scope of the result, maybe via an example. Say I take the polynomial endofunctor
Given that terminal coalgebras can be said to have cardinality , in which categories will I find such a thing?
In we have that the initial algebra for is the set of Motzkin trees. I guess the terminal coalgebra is the set of extended such trees, just as the initial algebra for is the natural numbers and the terminal coalgebra the extended natural numbers.
Re: In Search of Terminal Coalgebras
Of course, I should read again Tom’s introductory paper, and the longer two it introduces.