Capturing Goodwillie's derivative
Capturing Goodwillie's derivative
复制标题
捕获古德威利的导数
DOI：
10.1016/j.jpaa.2015.06.006
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发表时间：
2016
影响因子：
0.8
通讯作者：
Barnes D
中科院分区：
文献类型：
--
作者：
Barnes D
最近的工作Biedermann和Röndigs已经翻译古德威利的演算函子到语言的模型类别。他们的工作重点是对称多线性函子和衍生物出现只有简短的。在本文中，我们专注于理解作为右Quillen函子的一个新的模型范畴的衍生物。这直接类似于正交微积分中的韦斯导数的行为。这个新的类别的直接优点是，我们得到了一个简化的和更翔实的证明，n-齐次函子是由光谱分类的一个cnnn行动。在以后的论文中，我们将使用这个新的模型类别，给出一个正式的比较之间的正交演算和古德威利演算的函子。
Recent work of Biedermann and Röndigs has translated Goodwillie's calculus of functors into the language of model categories. Their work focuses on symmetric multilinear functors and the derivative appears only briefly. In this paper we focus on understanding the derivative as a right Quillen functor to a new model category. This is directly analogous to the behaviour of Weiss's derivative in orthogonal calculus. The immediate advantage of this new category is that we obtain a streamlined and more informative proof that the n-homogeneous functors are classified by spectra with a Σ n-action. In a later paper we will use this new model category to give a formal comparison between the orthogonal calculus and Goodwillie's calculus of functors.