AI 中文总结
本文为dagger (∞,1)-范畴构建单纯集模型，建立相关模型结构并证明伴随关系，引入酉核刻画等价关系，还与DCH反自伴随Joyal模型结构作比较。
AI 中文摘要
我们为 dagger (∞,1)-范畴开发单纯集模型。首先，在dagger单纯范畴上建立模型结构，其弱等价为本质上通过协调酉等价满射的局部弱等价；接着在dagger单纯集上构造dagger Joyal模型结构，并证明dagger刚性化-神经伴随是Quillen等价；随后引入酉核，用以内在刻画dagger Joyal等价；最后将该模型结构与DCH反自伴随Joyal模型结构进行比较。
英文摘要
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.
Comments45 pages. Comments welcome!
