Quasi-coproducts and accessible categories with wide pullbacks

Abstract

We establish a 2-categorical duality involving the 2-category .A,~ of all to-accessible categories with wide pullbacks, also known as locally tc-polypresentable categories, and of functors preserving ~¢-filtered colimits and wide puUbacks. 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,~ (1991). 18A35, 18B40, 18C99. Mathematics Subject Classifications