Corepresentations of equipped posets over the pair (F;G) are intro- duced and studied, where F ‰ G is a quadratic fleld extension. The reduction algorithms d and Completion for corepresentations (being in some intuitive sense dual to the known algorithms VII and Completion for representations) are built and investigated, with some applications. The generalized short ver- sions of Difierentiations VII and d VII for representations and corepresentations of equipped posets with additional relations are described.