Year: 2026
Type: preprint
Abstract: We develop simplicial-set models for dagger $(\infty,1)$-categories. We first establish a model structure on dagger simplicial categories whose weak equivalences are local weak equivalences that are essentially surjective up to coherently unitary equivalence. We then construct the dagger Joyal model structure on dagger simplicial sets and prove that the dagger rigidification--nerve adjunction is a Quillen equivalence. We next introduce the unitary core and use it to characterize dagger Joyal equivalences intrinsically. Finally, we compare the dagger Joyal model structure with the DCH anti-involutive Joyal model structure.
Source: arXiv (Cornell University)
Author: Akasaka, Keima
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204890248