Models for dagger (∞,1)-categories III: Univalent flagged dagger (∞,1)-categories and unitarily complete dagger Segal anima

@misc{akasaka2026models,
  title = {{Models for dagger $(\infty,1)$-categories III: Univalent flagged dagger $(\infty,1)$-categories and unitarily complete dagger Segal anima}},
  author = {Keima Akasaka},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17311},
  eprint = {2610.17311},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17311},
}

TY  - UNPB
TI  - Models for dagger (∞,1)-categories III: Univalent flagged dagger (∞,1)-categories and unitarily complete dagger Segal anima
AU  - Keima Akasaka
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.17311
UR  - https://arxiv.org/abs/2610.17311
AB  - We identify the (∞,1)-category presented by the dagger Bergner, dagger Joyal, and dagger Rezk models of Parts I and II with that of univalent flagged dagger (∞,1)-categories. We first construct a realization--nerve adjunction between reversal simplicial anima and Hermitian flags. We prove that its nerve restricts to an equivalence between flagged dagger (∞,1)-categories and dagger Segal anima, under which univalence corresponds to unitary completeness. We then construct the adjunctions for univalentization and Hermitian completion and identify univalentization with unitary completion.
ER  -