We study spans of cospans in a category C and explain how to horizontally and vertically compose these. When C is a topos and the legs of the spans are monic, these two forms of composition satisfy the interchange law. In this case there is a bicategory of objects, cospans, and `monic-legged' spans of cospans in C. One motivation for this construction is an application to graph rewriting.
Keywords: spans, cospans, bicategory, graph rewriting, adhesive category, network theory
2010 MSC: 18D05,68Q42,90B10
Theory and Applications of Categories, Vol. 33, 2018, No. 6, pp 131-147.