  Aggregating data in a database could also be called "integrating along
fibers": given functions $\pi\colon E\to D$ and $s\colon E\to R$, where
$(R,\circledast)$ is a commutative monoid, we want a new function $(\circledast
s)_\pi$ that sends each $d\in D$ to the "sum" of all $s(e)$ for which
$\pi(e)=d$. The operation lives alongside querying -- or more generally data
migration -- in typical database usage: one wants to know how much Canadians
spent on cell phones in 2021, for example, and such requests typically require
both aggregation and querying. But whereas querying has an elegant
category-theoretic treatment in terms of parametric right adjoints between
copresheaf categories, a categorical formulation of aggregation -- especially
one that lives alongside that for querying -- appears to be completely absent
from the literature.
  In this paper we show how both querying and aggregation fit into the
"polynomial ecosystem". Starting with the category $\mathbf{Poly}$ of
polynomial functors in one variable, we review the relatively recent results of
Ahman-Uustalu and Garner, which showed that the framed bicategory
$\mathbb{C}\mathbf{at}^\sharp$ of comonads in $\mathbf{Poly}$ is precisely the
right setting for data migration: its objects are categories and its
bicomodules are parametric right adjoints between their copresheaf categories.
We then develop a great deal of theory, compressed for space reasons, including
local monoidal closed structures, a coclosure to bicomodule composition, and an
understanding of adjoints in $\mathbb{C}\mathbf{at}^\sharp$. Doing so allows us
to derive interesting mathematical results, e.g.\ that the ordinary operation
of transposing a span can be decomposed into the composite of two more
primitive operations, and then finally to explain how aggregation arises,
alongside querying, in $\mathbb{C}\mathbf{at}^\sharp$.
