网表示的同伦理论
Homotopy theory of net representations
摘要：
发展了取值于闭对称monoidal模型范畴的（小）范畴上代数网表示的同伦理论。我们说明了如何每个态射的代数网确定一个变化的净奎伦附加模型类别之间的净表示，这是一个奎伦等价时，态射是一个弱等价。这些技术适用于同伦代数量子场论的上下文中的值在上链复合物。特别是，一个明确的建设，产生恒定的净表示麦克斯韦$p$ -形式上的一个固定的面向和面向时间的全球双曲洛伦兹流形。
英文摘要：
The homotopy theory of representations of nets of algebras over a (small) category with values in a closed symmetric monoidal model category is developed. We illustrate how each morphism of nets of algebras determines a change-of-net Quillen adjunction between the model categories of net representations, which is furthermore a Quillen equivalence when the morphism is a weak equivalence. These techniques are applied in the context of homotopy algebraic quantum field theory with values in cochain complexes. In particular, an explicit construction is presented that produces constant net representations for Maxwell $p$-forms on a fixed oriented and time-oriented globally hyperbolic Lorentzian manifold.
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