Bicategories of spans as generic bicategories

Abstract

In a bicategory of spans (an example of a 'generic bicategory') the factorization of a span (s,t) as the span (s,1) followed by (1,t) satisfies a simple universal property with respect to all factorizations in terms of the generic bicategory structure. Here we show that this universal property can in fact be used to characterize bicategories of spans. This characterization of spans is very different from the others in that it does not mention any adjointness conditions within the bicategory.