二维并行输运：组合学与函子性
Two-dimensional parallel transport : combinatorics and functoriality
摘要：
我们延长通常的概念平行运输沿路径三角形表面。路径的同伦被提升到一个具有连接的纤维范畴中，这在边界路径之上的纤维之间定义了一个函子。这些“扫描函子”传输纤维束的连接沿表面，而通常的连接传输群元素沿一个path.We表明，摆脱参数化，我们必须使用阿贝尔自由度。在一般的情况下，非阿贝尔的情况下，我们猜想，这种建设的顺利限制为我们提供了一组的扫描表面的表示。应用规范理论的建议。
英文摘要：
We extend the usual notion of parallel transport along a path to triangulated surfaces. A homotopy of paths is lifted into a fibered category with connection and this defines a functor between the fibers above the boundary paths. These "sweeping functors" transport fiber bundles with connection along a surface whereas usual connections transport a group element along a path. We show that to get rid of the parametrization, we must use Abelian degrees of freedom. In the general, non-Abelian case, we conjecture that the smooth limit of this construction provides us with representations of the group of diffeomorphisms of the swept surface. Applications to gauge theories are proposed.
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