Quasi-categories vs Segal spaces

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

Andre Joyal , Myles Tierney This is my paper · ORCID

classification math.AT

keywords segalquasi-categoriesspacescategoriescompleteequivalentquillen

verification ladder T0 review T1 audit T2 compute T3 formal

No signed human review yet.

0 comments

read the original abstract

We show that complete Segal spaces and Segal categories are Quillen equivalent to quasi-categories.

Forward citations

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

The Leibniz adjunction in homotopy type theory, with an application to simplicial type theory
math.CT 2026-01 accept novelty 8.0 of 10 full

A Segal type — a type with unique (2,1)-horn fillers — has unique fillers for every inner (n,k)-horn.
A homotopy theory of coherently commutative monoidal quasi-categories
math.CT 2019-08 conditional novelty 6.0 of 10

The paper constructs a symmetric monoidal closed model category of Gamma-spaces whose fibrant objects are coherently commutative monoidal quasi-categories, and proves Quillen equivalences with normalized Gamma-spaces ...