Abstract

In adhesive categories, pushouts along monomorphisms are Van Kampen (vk) squares, a special case of a more general notion called vk-diagram. Other examples of vk-diagrams include coproducts in extensive categories and strict initial objects. Extensive and adhesive categories characterise useful exactness properties of, respectively, coproducts and pushouts along monos and have found several applications in theoretical computer science. We show that the property of being vk is actually universal, not in C but in the bicategory of spans Span C. This theorem of pure category theory sheds light on the nature of spans and suggests promising generalisations of the theory of adhesive categories.

Citations