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math.CT2024
Transposing cartesian and other structure in double categories
Evan Patterson
The cartesian structure possessed by relations, spans, profunctors, and other such morphisms is elegantly expressed by universal properties in double categories. Though cartesian d…
math.CT2024
Representing Knowledge and Querying Data using Double-Functorial Semantics
Michael Lambert, Evan Patterson
Category theory offers a mathematical foundation for knowledge representation and database systems. Popular existing approaches model a database instance as a functor into the cate…
math.CT2024
Products in double categories, revisited
Evan Patterson
Products in double categories, as found in cartesian double categories, are an elegant concept with numerous applications, yet also have a few puzzling aspects. In this paper, we r…