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.
Directed Containers as Categories
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abstract
Directed containers make explicit the additional structure of those containers whose set functor interpretation carries a comonad structure. The data and laws of a directed container resemble those of a monoid, while the data and laws of a directed container morphism those of a monoid morphism in the reverse direction. With some reorganization, a directed container is the same as a small category, but a directed container morphism is opcleavage-like. We draw some conclusions for comonads from this observation, considering in particular basic constructions and concepts like the opposite category and a groupoid.
fields
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.