Sums of Lattices and a Relational Category

We introduce a new relational category of lattices, and an analogous category of complete lattices. These categories allow us to construct sums of (complete) lattices. While previous constructions used two functors (or, for complete lattices, a single functor that had an adjoint), we need only a single functor (and no additional property when complete lattices are considered). In the finite case, the present construction is easy to visualize.