---
title: "On pushouts of strict symmetric monoidal categories"
authors:
  - "Lucas Anderson"
  - "Ariel E. Rosenfield"
  - "Eric Yu"
year: 2026
venue: "arXiv:math.CT"
arxiv: "2609.08764"
doi: null
source: "https://arxiv.org/abs/2609.08764"
topics:
  - "curiosity"
  - "maths-foundations"
seed_rank: 1781
seed_batch: "curiosity-2026-09-11"
reviewed: "2026-09-11"
pool: "maths-foundations"
relevance_score: 9
lineage: symmetric-monoidal-pushouts
cites:
  - title: "On pushouts of strict symmetric monoidal categories"
    url: "https://arxiv.org/abs/2609.08764"
    year: 2026
    arxiv: "2609.08764"
    doi: null
see:
  - "117-a-survey-of-graphical-languages-for-monoidal-categories"
  - "1585-quantum-hopf-rigidity-in-symmetric-monoidal-categories"
  - "1469-string-diagrams-for-monoidal-categories-in-rocq"
---

# On pushouts of strict symmetric monoidal categories

## One-sentence takeaway

An explicit pushout of strict symmetric monoidal categories (strong monoidal functors) plus the fact that braided strong monoidal functors preserve central idempotents — aimed at modelling concurrency.

## Why it's lovely

Why you might love this: central idempotents in monoidal categories are a crisp algebraic handle on "independent subsystems," and pushouts are how you glue them. Explicit constructions here are rare and useful; the concurrency modelling intent is a welcome bridge toward process/effect semantics without leaving pure CT.

## Key ideas

- Explicit pushout construction for strict SMCs along strong monoidal functors.
- Any braided strong monoidal functor strongly preserves central idempotents.
- Corollary: lattice of central idempotents is isomorphic (as meet-semilattice) to that of the strictification.
- Motivated by modelling computational concurrency via central idempotents.

## Caveats

Strict SMC setting; weak/monoidal bicategorical pushouts remain harder. Concurrency application is motivational rather than a finished process calculus.

## Links

- arXiv abs: https://arxiv.org/abs/2609.08764
- PDF: https://arxiv.org/pdf/2609.08764.pdf