双变量纤维化、分解系统与张成空间的$\infty$-范畴
Two-variable fibrations, factorisation systems and $\infty$-categories of spans
AI总结：
本文在Barwick适当三元组框架下证明张成空间$\infty$-范畴的万有性质，引入正交适当三元组并证明其自等价性，进而统一推广了展开定理、正交分解系统、双变量纤维化及参数化伴随等多个范畴论结果。
摘要：
我们在Barwick适当三元组的一般性框架下证明了张成空间$\infty$-范畴的万有性质，明确描述了与张成函子对应的余笛卡尔纤维化，并证明后者限制在我们为此目的引入的正交适当三元组类上构成一个自等价。作为我们所发展机制的应用，我们给出了Barwick展开定理的简洁证明；证明了正交分解系统由笛卡尔纤维化产生当且仅当它构成适当三元组（推广了Lanari的工作）；将Barwick、Glasman和Nardin对偶（余）笛卡尔纤维化的描述推广到双变量纤维化；明确描述了参数化伴随（推广了Torii的工作）；识别了分类一个$(\infty,2)$-范畴的映射范畴函子的正交纤维化（建立在Abellán Garcia和Stern的工作之上）；形式地将$\infty$-范畴的$\infty$-范畴上恒等函子的反拉直化等同于一个点的（反）松弛下范畴；并推导出Yoneda嵌入的某种自然性性质（回答了Clausen的一个问题）。
英文摘要：
We prove a universal property for $\infty$-categories of spans in the generality of Barwick's adequate triples, explicitly describe the cocartesian fibration corresponding to the span functor, and show that the latter restricts to a self-equivalence on the class of orthogonal adequate triples, which we introduce for this purpose. As applications of the machinery we develop we give a quick proof of Barwick's unfurling theorem, show that an orthogonal factorisation system arises from a cartesian fibration if and only if it forms an adequate triple (generalising work of Lanari), extend the description of dual (co)cartesian fibrations by Barwick, Glasman and Nardin to two-variable fibrations, explicitly describe parametrised adjoints (extending work of Torii), identify the orthofibration classifying the mapping category functor of an $(\infty,2)$-category (building on work of Abellán Garcia and Stern), formally identify the unstraightenings of the identity functor on the $\infty$-category of $\infty$-categories with the (op)lax under-categories of a point, and deduce a certain naturality property of the Yoneda embedding (answering a question of Clausen).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
