distributive squares

Hi all, My student Clovis Eberhart and I were led to consider certain ‘distributive’ squares of categories and functors, in the sense that doing left then right Kan extension (of presheaves) along one side is isomorphic to doing right then left along the other. Does anyone please know if such squares have been studied somewhere? Best wishes to all, Tom [For admin and other information see: http://www.mta.ca/~cat-dist/ ]