6 papers · 1 filter
Twisted double functors and loosely discrete opfibrations
Michael Lambert, David Jaz Myers, Evan Patterson
Various situations in the theory and applications of double categories, ranging from a loose Yoneda theory and loose compact closure to double-operadic systems theory, require a no…
Presheaves on lax double functors; or, Instances of models of double theories
Kevin Carlson, Evan Patterson
We introduce a notion of (co)presheaf on a lax double functor , which we generally call an instance. In the terminology of double-categorical logic, a lax double functor valued…
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…
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…
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…
Cartesian double theories: A double-categorical framework for categorical doctrines
Michael Lambert, Evan Patterson
The categorified theories known as "doctrines" specify a category equipped with extra structure, analogous to how ordinary theories specify a set with extra structure. We introduce…