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