Sketches and lattices

Dear Category Theorists, Does anyone know whether any work has been done on sketches where all diagrams are required to commute - i.e. the models are functors from a poset to the given category. I'm particularly interested in the case where the sketch is in fact a lattice, and where we require every avb--------------a | | | | | | b--------------a^b should be sent to a pullback. Thanks for any pointers you can give. Toby