Constructing categories of (co)relations via pushout
On the way to providing a presentation of the category LinRel of linear relations, Bonchi, Sobocinski, and Zanasi showed that LinRel is the pushout of the spanCospan(Vect) <--- Vect+Vect^op ---> Span(Vect),
where Vect is the category of vector spaces and linear maps. In this talk, I will explore the conditions under which Vect may be replaced with other categories, so that the pushout of the analogous span is nonetheless, like LinRel, a category of (co)relations. This unifies various observations in the literature, and provides a modular way to derive presentations for such categories.