Functorial aggregation

TL;DR

This paper explores polynomial comonads and bicomodules to model database aggregation and querying within a categorical framework, revealing universal constructions and their applications in data migration.

Contribution

It introduces a categorical approach to database aggregation using polynomial comonads and bicomodules, connecting universal constructions with data migration functors.

Findings

Polynomial bicomodules correspond to parametric right adjoint functors.

Universal constructions are characterized within the bicategory of categories.

The framework models database aggregation and querying cohesively.

Abstract

We study polynomial comonads and polynomial bicomodules. Polynomial comonads amount to categories. Polynomial bicomodules between categories amount to parametric right adjoint functors between corresponding copresheaf categories. These may themselves be understood as generalized polynomial functors. They are also called data migration functors because of applications in categorical database theory. We investigate several universal constructions in the framed bicategory of categories, retrofunctors, and parametric right adjoints. We then use the theory we develop to model database aggregation alongside querying, all within this rich ecosystem.