Many categorical models of linear logic with fixed points arise as total categories over the category Rel of sets and relations. They are form ∫Q, the Grothendieck category for a functor Q : Rel -> Pos. We will define the concepts of fixed points and Grothendieck category and then we give a result to lift functor from the base category to the total category and studies also how to lift fixed points. In particular, the category of coalgebras for the lifted functor is a total category, and when Q factors through SLatt, the category of posets with joins and maps that preserve them, we found the same result.