论文标题
物种中煤桥的共同体学
The cohomology of coalgebras in species
论文作者
论文摘要
Aguiar和Mahajan引入了Joyal扭曲的结骨的共同体学理论，对其第二个共同体学组的计算特别感兴趣，这引起了它们的变形。我们在扭曲的代数和山地之间使用Koszul二元性理论在扭曲的山地上引起了其共同体学理论，从而对其进行了新的替代描述，尤其允许其有效的计算。我们在包括Aguiar和Mahajan提出的示例中完全计算它，并获得结构结果：特别是，我们研究其乘法结构并提供Künneth公式。
Aguiar and Mahajan introduced a cohomology theory for the twisted coalgebras of Joyal, with particular interest in the computation of their second cohomology group, which gives rise to their deformations. We use the Koszul duality theory between twisted algebras and coalgebras on the twisted coalgebra that gives rise to their cohomology theory to give a new alternative description of it which, in particular, allows for its effective computation. We compute it completely in various examples, including those proposed by Aguiar and Mahajan, and obtain structural results: in particular, we study its multiplicative structure and provide a Künneth formula.
