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Constructing categories of (co)relations via pushout

Brendan Fong

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 span 
                 Cospan(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.

This is based on joint work with Fabio Zanasi; see https://arxiv.org/abs/1703.08247.

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