On geometric and finitary sketches

A survey of results on categories which can be sketched by a finitary sketch (i.e., a sketch with finite limit and finite colimit specifications) or by a geometric sketch (i.e., a sketch with finite limit specifications and arbitrary colimit specifications) is presented. Transitive-hull theories are introduced which precisely characterize finitarily sketchable categories.Financial support of the Grant Agency of the Czech Republic under the grant No 201/93/0950 is gratefully acknowledged.