  Generalizing different variants of "graph conditions and constraints" as well
as "universal constraints" and "negative universal constraints" in the Diagram
Predicate Framework (DPF), we introduce for arbitrary categories $\mathbf{Cxt}$
and "statement" functors $\mathtt{Stm}:\mathbf{Cxt}\to\mathbf{Set}$ general
first-order sketch conditions and constraints. Sketches are used in DPF to
formalize different kinds of diagrammatic software models. We discuss the use
of sketch constraints for describing the syntactic structure of sketches. We
outline the use of sketch constraints to deduce knowledge implicitly given in a
sketch as well as procedures to deduce sketch constraints from given sketch
constraints. We use the simple but paradigmatic modeling formalism "Category
Theory" as running example.
