论文标题
净表示的同义理论
Homotopy theory of net representations
论文作者
论文摘要
在封闭的对称单体模型类别中，代数类别的代数网的表达式的同遵封理论已开发出来。我们说明了代数网的每个形态如何决定净表示模型类别之间的净变化quillen邻接，当形态是较弱的等效性时，净表示的模型类别也是quillen等价的。这些技术应用于同型代数量子场理论的背景下，在Cochain复合物中具有值。特别是，提出了一种明确的结构，该结构在固定的面向固定的和面向时间的全球劳伦斯歧管上产生了麦克斯韦$ p $ forms的恒定净表示。
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.
