  A theory of sketches for arithmetic universes (AUs) is developed.
  A restricted notion of sketch, called here "context", is defined with the
property that every non-strict model is uniquely isomorphic to a strict model.
This allows us to reconcile the syntactic, dealt with strictly using universal
algebra, with the semantic, in which non-strict models must be considered.
  For any context T, a concrete construction is given of the AU AU<T> freely
generated by it.
  A 2-category Con of contexts is defined, with a full and faithful 2-functor
to the 2-category of AUs and strict AU-functors, given by T |-> AU<T>. It has
finite pie limits, and also all pullbacks of a certain class of "extension"
maps. Every object, morphism or 2-cell of Con is a finite structure.
