范畴结构的Koszul性：2-网范畴
Towards Koszulity for categorical structures: category of 2-nets
中文总结 AI 辅助
本文针对Batanin和Markl的Koszul对偶理论无法直接应用于n-树operad范畴的问题，提出2-网范畴，将该理论扩展到2-树情形，证明其为含2-树满子范畴的operad范畴且态射可分解为初等态射链。
中文摘要 AI 辅助
近期，Batanin和Markl以Ginzburg-Kapranov的精神发展了一般-operad范畴上的operad的Koszul对偶理论，但该方法无法直接应用于用于描述范畴结构的n-树的operad范畴。本文提出（局部常值）2-网范畴，解决了将该理论扩展到2-树情形的主要困难；该2-网范畴是包含2-树作为满子范畴的operad范畴，且任意2-网间的态射均可分解为初等态射链。
英文摘要
Recently Batanin and Markl developed a theory of Koszul duality for operads over a general operadic category in the spirit of Ginzburg-Kapranov. However, their approach doesn't apply directly to the operadic category of n-trees, which are used to describe categorical structures. In this paper we present a category of (locally constant) 2-nets which addresses the main difficulty of extending their theory to the case of 2-trees. Specifically, our category of 2-nets is an operadic category containing 2-trees as a full subcategory, and every map between 2-nets admits a factorization into a chain of elementary maps.
