论文标题
自由代数在一天卷积上
Free algebras through Day convolution
论文作者
论文摘要
在我们先前论文的基础上，我们研究了由有限产品给出的Segal条件，这些条件由我们称为笛卡尔模式的结构确定。我们在此环境中对预选时进行了一天的卷积，并使用它来提供适用于自由代数和其他左伴随的colimit公式的条件。这专门为Lurie提供了一个简单的证明，以证明Lurie的左KAN扩展名和对称$ \ Infty $ -operads的免费代数。
Building on the foundations in our previous paper, we study Segal conditions that are given by finite products, determined by structures we call cartesian patterns. We set up Day convolution on presheaves in this setting and use it to give conditions under which there is a colimit formula for free algebras and other left adjoints. This specializes to give a simple proof of Lurie's results on operadic left Kan extensions and free algebras for symmetric $\infty$-operads.
