论文标题
比较正交和统一函子cyculi
Comparing the orthogonal and unitary functor calculi
论文作者
论文摘要
正交和统一的结石提供了一种从实际或复杂的内部产品空间类别研究到基于拓扑空间类别的方法。我们从真实和复杂的内部产品空间之间的络合化相连构造函数。这些允许在微积分版本的版本之间移动，并在两种骨会产生的泰勒塔之间进行比较。我们表明，当输入的正交函子是弱多项式时，函子的泰勒塔通过实现限制，而函子的受限泰勒塔也同意弱等效性。我们进一步提高了塔的同质级别比较与Quillen函子的交换图，该Quillen函数将型的模型类别与正交演算以及单一演算的模型类别相关联。
The orthogonal and unitary calculi give a method to study functors from the category of real or complex inner product spaces to the category of based topological spaces. We construct functors between the calculi from the complexification-realification adjunction between real and complex inner product spaces. These allow for movement between the versions of calculi, and comparisons between the Taylor towers produced by both calculi. We show that when the inputted orthogonal functor is weakly polynomial, the Taylor tower of the functor restricted through realification and the restricted Taylor tower of the functor agree up to weak equivalence. We further lift the homotopy level comparison of the towers to a commutative diagram of Quillen functors relating the model categories for orthogonal calculus and the model categories for unitary calculus.
