Pith. sign in

REVIEW 1 cited by

$\omega$-weak equivalences between weak $\omega$-categories

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2406.13240 v3 pith:FEVFDAZS submitted 2024-06-19 math.CT

classification math.CT
keywords omegaweakequivalencescategoriesstrictclassdefinedessential
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We study $\omega$-weak equivalences between weak $\omega$-categories in the sense of Batanin-Leinster. Our $\omega$-weak equivalences are strict $\omega$-functors satisfying essential surjectivity in every dimension, and when restricted to those between strict $\omega$-categories, they coincide with the weak equivalences in the model category of strict $\omega$-categories defined by Lafont, M\'etayer, and Worytkiewicz. We show that the class of $\omega$-weak equivalences has the 2-out-of-3 property. We also consider a generalisation of $\omega$-weak equivalences, defined as weak $\omega$-functors (in the sense of Garner) satisfying essential surjectivity, and show that this class also has the 2-out-of-3 property.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Semi-strictification of $(\infty, n)$-categories

    math.CT 2025-06 conditional novelty 8.0 of 10

    Every weak (∞,n)-category embeds into a semi-strict algebraic model via an acyclic cofibration, forming the derived unit of a Quillen equivalence between weak model categories.

Pith tools