Polynomial comonads amount to categories and polynomial bicomodules amount to parametric right adjoint functors, enabling a model of database aggregation alongside querying inside a framed bicategory of categories, retrofunctors, and parametric right adjoints.
String Diagrams For Double Categories and Equipments
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
A popular graphical calculus for monoidal categories makes computations tactile and intuitive. Complicated diagram chases can be expressed in a few pictures and discovered by playing with a shoelace. Joyal and Street's proof of the soundness of this calculus says that any deformation of a diagram, any bending of the strings, describes the same morphism. In this paper, we extend the graphical calculus to double categories and proarrow equipments in order to bring the string diagrammatic method to formal category theory. Our main theorem proves this calculus sound with the help of Dawson and Pare's results on composition in double categories.
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math.CT 1years
2021 1verdicts
UNVERDICTED 1representative citing papers
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Functorial aggregation
Polynomial comonads amount to categories and polynomial bicomodules amount to parametric right adjoint functors, enabling a model of database aggregation alongside querying inside a framed bicategory of categories, retrofunctors, and parametric right adjoints.