A generalization of the concept of sketch

AbstractThis paper introduces an extension of the concept of sketch, called a form, which allows the specification of entities other than limits and colimits in a model. A form can require that a diagram become (in a model) an instance of any categorial construction specifiable in an essentially algebraic way. Constructions which can be specified in this way include function space objects in and reflexive objects in a cartesian closed category, power objects in a topos, and list objects in a locos. This generalization is motivated by the desire to specify functional programming languages by sketches