Abstract We describe a category of undirected graphs which comes equipped with a faithful functor into the category of (colored) modular operads. The associated singular functor from modular operads to presheaves is fully faithful, and its essential image can be classified by a Segal condition. This theorem can be used to recover a related statement, due to Andre Joyal and Joachim Kock, concerning a larger category of undirected graphs whose functor to modular operads is not just faithful but also full.

中文翻译：

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模块化操作数和神经定理

摘要 我们将配备忠实函子的无向图类别描述为（彩色）模操作数类别。从模操作数到预绳的相关奇异函子是完全忠实的，其本质形象可以通过西格尔条件进行分类。由于 Andre Joyal 和 Joachim Kock，该定理可用于恢复相关陈述，该陈述涉及更大类别的无向图，其对模操作数的函子不仅忠实而且完整。