# Functorial aggregation

arXiv: https://arxiv.org/abs/2111.10968 · HTML: https://mlsanity.com/paper/2111.10968/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Nov 2021.

## Built on by (most cited first, 1 of 1)

- [Space-time tradeoffs of lenses and optics via higher category theory](https://mlsanity.com/paper/2209.09351/) (2022)

## Abstract (arXiv)

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.