---
title: "Quantification in Double-Categorical Database Schemas"
authors:
  - "Michael Lambert"
year: 2026
venue: "arXiv:math.CT"
arxiv: "2608.00913"
doi: null
source: "https://arxiv.org/abs/2608.00913"
topics:
  - "curiosity"
  - "maths-foundations"
  - "embedded-scripting"
seed_rank: 1619
seed_batch: "curiosity-2026-09-07"
reviewed: "2026-09-07"
pool: "maths-foundations"
relevance_score: 10
lineage: applied-category-theory
cites:
  - title: "Quantification in Double-Categorical Database Schemas"
    url: "https://arxiv.org/abs/2608.00913"
    year: 2026
    arxiv: "2608.00913"
    doi: null
see:
  - "1029-a-rig-of-transformations"
---

# Quantification in Double-Categorical Database Schemas

## One-sentence takeaway

Double-categorical database schemas gain universal quantification (right adjoints to substitution), unlocking relational division and modal operators via tabulators.

## Why it's lovely

Why you might love this: databases as double categories, then *add ∀* as a right adjoint to substitution — relational division becomes a categorical construct, and modal operators fall out of tabulators. Applied CT that smells like a query language.

## Key ideas

- Enrich double-categorical schemas with right adjoints to substitution (universal quantification).
- Relational division expressible in that language.
- Right adjoints + tabulators interpret modal operators.
- Schema morphisms / queries as structured categorical maps.

## Caveats

Theoretical schema language; not a drop-in SQL engine. Double-category fluency required.

## Implications for Broadside

Rare database↔CT bridge for Broadside/ano: quantification and division as adjoint structure rather than stringly-typed query hacks.

## Links

- arXiv abs: https://arxiv.org/abs/2608.00913
- PDF: https://arxiv.org/pdf/2608.00913.pdf