Cartesian closed exact completions (Q1124976)

The author introduces and investigates the concepts of small functors and Cartesian preclosed categories. His main result states that a category \({\mathcal C}\), under suitable assumptions, is Cartesian preclosed iff its exact completion is Cartesian closed. As an important application he demonstrates that the exact completion of the category \({\mathcal T}op\) of topological spaces and continuous maps is Cartesian closed.