Lax colimits and free fibrations in ∞-categories
Lax colimits and free fibrations in ∞-categories
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∞ 类别中的宽松余界和自由纤维
DOI：
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发表时间：
2017
期刊：
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通讯作者：
T. Nikolaus
中科院分区：
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作者：
David Gepner;R. Haugseng;T. Nikolaus
。我们定义并讨论了∞范畴图的松弛极限和加权极限，并证明了函子对应的笛卡儿颤振由它的松弛极限给出。一个关键的成分，独立的兴趣，是一个简单的表征上的自由笛卡儿振动的函子的∞-范畴。作为这些结果的一个应用，我们证明了2-可表征函子在幂次下是守恒的，并且证明了可表征笛卡尔振动之间的总空间是可表征的，将Makkai和Par´e的一个定理推广到∞-范畴集合。最后，在附录中，我们观察到(2,1)-范畴之间的伪函子通过Duskin神经产生∞-范畴之间的函子。和Duskin神经。
. We define and discuss lax and weighted colimits of diagrams in ∞ -categories and show that the coCartesian fibration corresponding to a functor is given by its lax colimit. A key ingredient, of independent interest, is a simple characterization of the free Cartesian fibration on a functor of ∞ -categories. As an application of these results, we prove that 2-representable functors are preserved under exponentiation, and also that the total space of a presentable Cartesian fibration between is presentable, generalizing a theorem of Makkai and Par´e to the ∞ -categories setting. Lastly, in an appendix, we observe that pseudofunctors between (2,1)-categories give rise to functors between ∞ -categories via the Duskin nerve. setting and the Duskin nerve.