Simplicial Nerve of an A ∞-category
Simplicial Nerve of an A ∞-category
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A ∞ 类的单纯神经
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发表时间：
2017
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通讯作者：
Giovanni Faonte
中科院分区：
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作者：
Giovanni Faonte
本文引入了一个函子，称为A∞范畴的单纯神经，它定义在取值于单纯集的（小）A∞范畴上.证明了A∞-范畴的神经是J.Lurie [Lur 1]意义下的∞-范畴。该构造推广了[Lur 2]中给出的微分分次范畴的神经构造。证明了若微分分次范畴在A. I. Bondal-M.Kapranov [Bo-Ka]意义下是预三角化的，则它的神经在J.Lurie [Lur 2]意义下是稳定的∞-范畴.
In this paper we introduce a functor, called the simplicial nerve of an A∞category, defined on the category of (small) A∞-categories with values in simplicial sets. We prove that the nerve of an A∞-category is an ∞-category in the sense of J.Lurie [Lur1]. This construction generalize the nerve construction for differential graded categories given in [Lur2]. We prove that if a differential graded category is pretriangulated in the sense of A.I.Bondal-M.Kapranov [Bo-Ka], then its nerve is a stable ∞-category in the sense of J.Lurie [Lur2].