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Models for dagger (∞,1)-categories II: Dagger complete Segal spaces and the Joyal--Tierney equivalence
Abstract
Building on the dagger Bergner and dagger Joyal models constructed in Part I, we develop simplicial-space models for dagger (∞,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.
Related
- Models for dagger (∞,1)-categories III: Univalent flagged dagger (∞,1)-categories and unitarily complete dagger Segal anima
- Equivalence of categories of bivariant K-theory for C*-algebras over topological spaces via reflection functors
- Models for dagger (∞,1)-categories I: Dagger simplicial sets and unitary cores
- Characterizing (Co)Free Dagger Categories
- Dagger Categories in Riemannian Geometry
BibTeX
@misc{akasaka2026models,
title = {{Models for dagger $(\infty,1)$-categories II: Dagger complete Segal spaces and the Joyal--Tierney equivalence}},
author = {Keima Akasaka},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06935},
eprint = {2609.06935},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06935},
}
RIS
TY - UNPB
TI - Models for dagger (∞,1)-categories II: Dagger complete Segal spaces and the Joyal--Tierney equivalence
AU - Keima Akasaka
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.06935
UR - https://arxiv.org/abs/2609.06935
AB - Building on the dagger Bergner and dagger Joyal models constructed in Part I, we develop simplicial-space models for dagger (∞,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.
ER -