The paper addresses a notion of configuring systems, constructing them from specified component parts with stipulated sharing. This notion is independent of any underlying specification language and has been abstractly identified with the taking of colimits in category theory. In particular, Oriat has shown how to use a category of diagrams Diag(C) to express colimits of primitive specifications from a category C. Mathematically it is known that these can equally well be expressed by presheaves over C and the present paper applies this idea to configuration. We develop an algebraic account of presheaves, and show that Oriat's category Diag(C) is equivalent to the category of finitely presented presheaves over C. The presheaf structure is interpreted in terms of instances of specifications and instance reduction and a configuration language is outlined that expresses precisely the finite presentations of presheaves but also describes configuration in a natural way.