AI 中文总结
该研究将重写理论方法应用于拟范畴层面，通过模型结构转换得到弱(∞,1)-范畴的Amick-Groves-Squier型表示，并给出拟范畴理论相关应用。
AI 中文摘要
我们证明了建立协调性定理的重写理论方法可应用于拟范畴层面。更准确地说，对任何可由合流重写系统表示的范畴C，我们证明其对应的弱(∞,1)-范畴可具有Amick-Groves-Squier型表示，其生成元对应该重写系统的（部分）临界分支。这完全源于将K. Brown关于通常同调Anick-Groves-Squier表示的单纯证明，从Kan-Quillen模型结构重新解释为Joyal模型结构。我们将此结果应用于拟范畴理论的若干方面，包括针对无环平面范畴论图的相对一般协调性定理，以及Dwyer映射的推出是同伦推出的新证明。
英文摘要
We show that the methods of rewriting theory to establish coherence theorems can applied at the level of quasicategories. More precisely, for any category C which admits a presentation by a convergent rewrite system, we show that the corresponding weak (infinity,1)-category admits an Amick-Groves-Squier style presentation whose generators correspond to (some of) the critical branchings of the rewrite system. This follows entirely from reinterpreting K. Brown's simplicial proof of the usual homological Anick-Groves-Squier presentation in terms of the Joyal model structure instead of the Kan-Quillen model structure. We give several applications of this to the theory of quasicategories, including a relatively general coherence theorem for loop-free planar category theoretic diagrams and a new proof that pushout of Dwyer maps are homotopy pushouts.
Comments34 pages
