A Final Coalgebra Theorem

By the Final Coalgebra Theorem of Aczel and Mendler, every endofunctor of the category of sets has a final coalgebra, which, however, may be a proper class. We generalise this to all ‘well-behaved’ categories ${\frak K}$. The role of the category of ...

We define the continuum up to order isomorphism, and hence up to homeomorphism via the order topology, in terms of the final coalgebra of either the functor NX, product with the set of natural numbers, or the functor 1+NX. This makes an attractive ...

For deterministic systems, expressed as coalgebras over polynomial functors, every tree t (an element of the final coalgebra) turns out to represent a new coalgebra A_t. The universal property of this family of coalgebras, resembling freeness, is that ...