Models for dagger (∞,1)-categories I: Dagger simplicial sets and unitary cores

@misc{akasaka2026models,
  title = {{Models for dagger $(\infty,1)$-categories I: Dagger simplicial sets and unitary cores}},
  author = {Keima Akasaka},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29730},
  eprint = {2608.29730},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29730},
}

TY  - UNPB
TI  - Models for dagger (∞,1)-categories I: Dagger simplicial sets and unitary cores
AU  - Keima Akasaka
PY  - 2026
DA  - 2026/08/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.29730
UR  - https://arxiv.org/abs/2608.29730
AB  - We develop simplicial-set models for dagger (∞,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.
ER  -