树、图与聚合：组合曲面拓扑、几何与代数的范畴透视
Trees, graphs and aggregates: a categorical perspective on combinatorial surface topology, geometry, and algebra
摘要：
以费曼范畴的角度来看，曲面几何的几个关键方面推导出组合结构与图形。这提供了一个直接的路线，从组合的图形字符串拓扑运算，通过拓扑，几何和代数。特别是，列入树到图和解剖图到聚集产生一个简洁的形式主义循环和模块操作，以及他们的多环和表面类型的概括。后者在二维拓扑域论和弦拓扑学中占有突出地位。范畴观点允许我们使用费曼操作的左Kan扩展作为有效的计算工具。计算涉及的结构图，预计将是独立的利益的某些类别的研究。
英文摘要：
Taking a Feynman categorical perspective, several key aspects of the geometry of surfaces are deduced from combinatorial constructions with graphs. This provides a direct route from combinatorics of graphs to string topology operations via topology, geometry and algebra. In particular, the inclusion of trees into graphs and the dissection of graphs into aggregates yield a concise formalism for cyclic and modular operads as well as their polycyclic and surface type generalizations. The latter occur prominently in two-dimensional topological field theory and in string topology. The categorical viewpoint allows us to use left Kan extensions of Feynman operations as an efficient computational tool. The computations involve the study of certain categories of structured graphs which are expected to be of independent interest.
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