---
title: "Rewriting and presentations of quasicategories"
authors:
  - "Simon Henry"
year: 2026
venue: "arXiv:math.CT"
arxiv: "2608.02529"
doi: null
source: "https://arxiv.org/abs/2608.02529"
topics:
  - "curiosity"
  - "maths-foundations"
  - "embedded-scripting"
seed_rank: 1618
seed_batch: "curiosity-2026-09-07"
reviewed: "2026-09-07"
pool: "maths-foundations"
relevance_score: 9
lineage: higher-categories-rewriting
cites:
  - title: "Rewriting and presentations of quasicategories"
    url: "https://arxiv.org/abs/2608.02529"
    year: 2026
    arxiv: "2608.02529"
    doi: null
see:
  - "1027-a-critical-pair-enumeration-algorithm-for-string-diagram-rewriting"
---

# Rewriting and presentations of quasicategories

## One-sentence takeaway

Convergent rewrite presentations of ordinary categories lift to coherent presentations of the corresponding quasicategory — rewriting theory as ∞-coherence.

## Why it's lovely

Why you might love this: critical-pair / convergent rewriting is how you prove coherence classically; Henry shows the same toolkit speaks quasicategories. String-diagram critical pairs (1027) meet (∞,1)-presentations.

## Key ideas

- Start from a category with a convergent rewrite-system presentation.
- The associated weak (∞,1)-category admits a coherent presentation inherited from the rewrite system.
- Rewriting methods → coherence theorems at quasicategory level.
- Bridge between combinatorial rewriting and higher-categorical presentations.

## Caveats

Needs a convergent presentation of the 1-category first; not automatic for arbitrary quasicategories.

## Implications for Broadside

Directly adjacent to ano/language coherence instincts and the string-diagram critical-pair card (1027): rewrite systems as a path to higher coherence.

## Links

- arXiv abs: https://arxiv.org/abs/2608.02529
- PDF: https://arxiv.org/pdf/2608.02529.pdf