Models for dagger $(\infty,1)$-categories II: Dagger complete Segal spaces and the Joyal--Tierney equivalence
Year: 2026
Type: preprint
Abstract: Building on the dagger Bergner and dagger Joyal models constructed in Part I, we develop simplicial-space models for dagger $(\infty,1)$-categories. We first construct a homotopically constant resolution model and a model structure for unitarily complete dagger Segal spaces. A change-of-index adjunction compares the two presentations of dagger simplicial spaces. We then prove a dagger analogue of the Joyal--Tierney Quillen equivalence. Together with Part I, these results give a chain of Quillen equivalences between the dagger Bergner, dagger Joyal, and dagger Rezk models.
Source: arXiv (Cornell University)
Author: Akasaka, Keima
Institution: Chiba University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212083804