论文标题
合成纤维的内部总和$（\ infty，1）$ - 类别
Internal sums for synthetic fibered $(\infty,1)$-categories
论文作者
论文摘要
我们给出有关（内部）$（\ infty，1）$类别的分致的结构性结果。这包括Moens定理的更高版本，表征了笛卡尔分歧，又称稳定的稳定性和与Lex碱基上的脱节和内部总和为Lex Foundors的Artin Gluings。 由于Streicher，我们还将对Moens定理的广义版本进行处理，这不需要Beck-Chevalley条件。 此外，我们还表明，在这种情况下，Moens纤维可以通过Zawadowski引起的条件来表征。 我们的总体说明是遵循Streicher对纤维类别理论的介绍，将结果推广到在合成环境中提出的内部，高级案例。 也就是说，我们在简单同义类型理论中工作，Riehl和Shulman已将其作为一种逻辑系统介绍，以理解内部$（\ Infty，1）$ - 类别，被解释为任何给定的Grothendieck-Rezk-Rezk-Rezk-rezk--rezk--lurie $（\ infty，1）$ - topos。
We give structural results about bifibrations of (internal) $(\infty,1)$-categories with internal sums. This includes a higher version of Moens' Theorem, characterizing cartesian bifibrations with extensive aka stable and disjoint internal sums over lex bases as Artin gluings of lex functors. We also treat a generalized version of Moens' Theorem due to Streicher which does not require the Beck--Chevalley condition. Furthermore, we show that also in this setting the Moens fibrations can be characterized via a condition due to Zawadowski. Our account overall follows Streicher's presentation of fibered category theory à la Bénabou, generalizing the results to the internal, higher-categorical case, formulated in a synthetic setting. Namely, we work inside simplicial homotopy type theory, which has been introduced by Riehl and Shulman as a logical system to reason about internal $(\infty,1)$-categories, interpreted as Rezk objects in any given Grothendieck--Rezk--Lurie $(\infty,1)$-topos.
