---
title: "A model structure for cartesian 2-fibrations"
authors:
  - "Cesar Bardomiano Martinez"
  - "Jana K. Nickel"
  - "Maru Sarazola"
  - "Daniel Teixeira"
  - "Santiago Toro Oquendo"
  - "Paula Verdugo"
year: 2026
venue: "arXiv:math.CT"
arxiv: "2609.11759"
doi: null
source: "https://arxiv.org/abs/2609.11759"
topics:
  - "curiosity"
  - "maths-foundations"
  - "category-theory"
  - "homotopy-theory"
seed_rank: 1831
seed_batch: "curiosity-2026-09-15"
reviewed: "2026-09-15"
pool: "maths-foundations"
relevance_score: 10
lineage: cartesian-2-fibrations
cites:
  - title: "A model structure for cartesian 2-fibrations"
    url: "https://arxiv.org/abs/2609.11759"
    year: 2026
    arxiv: "2609.11759"
    doi: null
see: []
---

# A model structure for cartesian 2-fibrations

## One-sentence takeaway

Marked 2-categories carry a model structure whose fibrant objects present cartesian 2-fibrations, replacing much weak-coherence bookkeeping by a strict homotopical model.

## Why it's lovely

Why you might love this: indexed categories via cartesian 2-fibrations usually drown in coherence. Marking 2-categories and building a model structure lets straightening / comprehension live in a Quillen world — the same move that made quasicategories tractable, now one dimension up for people who index things for a living.

## Key ideas

- Cartesian 2-fibrations as a model of indexed categories.
- Marked 2-categories record the cartesian lifts strictly enough for a model structure.
- Homotopical replacement for classical straightening coherence data.
- Targets (∞,2)-adjacent bookkeeping without full ∞-machinery in the paper's surface.

## Caveats

Model-category foundations; comparison functors to fully weak (∞,2) presentations may still be needed for applications. No preexisting Broadside stem for 2-fibrations — see left empty rather than invented.

## Links

- arXiv abs: https://arxiv.org/abs/2609.11759
- PDF: https://arxiv.org/pdf/2609.11759.pdf