[Complement Toposes](http://philosophy.unimelb.edu.au/ajl/2010/2010_9.pdf) are dual in a sense to (elementary) Toposes and are expected to have typed higher paraconsistent logic as its internal language (as dual intuitionistic logic is paraconsistent).

Now one of the key examples of Toposes are Presheaf & Sheaf Toposes. Is there a corresponding analogue for Complement Toposes?