# Is there a category of non-well-founded sets?

Is there a category (in the category theory sense) of non-well-founded sets (something analogous to Set, the category of sets), and has it been (well-)studied? Any references are appreciated.

• Thank you Neel and Mike for your answers. I found the nLab notes helpful, as well as <a href="plato.stanford.edu/entries/nonwellfounded-set-theory/… section</a> of the SEP article. Sorry, though, I think I meant to ask a more open-ended question, perhaps unsuitable for mathoverflow. I am interested in references where a category of non-well-founded sets is used as an alternative to the category of sets. – Noam Zeilberger Feb 4 '10 at 22:41