Quasi-coproducts and accessible categories with wide pullbacks

We establish a 2-categorical duality involving the 2-category A of all -accessible categories with wide pullbacks, also known as locally -polypresentable categories, and of functors preserving -filtered colimits and wide pullbacks. Commutation of wide pullbacks with so-called quasi-coproducts in Set is the basic ingredient to this duality, which leads to a full characterization of categories of type Wdpb Filt (A, Set)=A The first author acknowledges financial assistance from a special research grant of the Faculty of Arts at York University. The second author is partially supported by an NSERC operating grant.Presented at the European Colloquium of Category Theory, Tours, France, 25–31 July 1994.