Models of non-well-founded sets via an indexed final coalgebra theorem

Benno van den Berg, Federico de Marchi
2007 Journal of Symbolic Logic (JSL)  
The paper uses the formalism of indexed categories to recover the proof of a standard final coalgebra theorem, thus showing existence of final coalgebras for a special class of functors on finitely complete and cocomplete categories. As an instance of this result, we build the final coalgebra for the powerclass functor, in the context of a Heyting pretopos with a class of small maps. This is then proved to provide models for various non-well-founded set theories, depending on the chosen axiomatisation for the class of small maps.
doi:10.2178/jsl/1191333841 fatcat:k3ptfzcre5btxktbcsae7stmfq