OPERADS AS POLYNOMIAL 2-MONADS
OPERADS AS POLYNOMIAL 2-MONADS
复制标题
作为多项式 2-单子的运算
DOI：
--
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Mark Weber
中科院分区：
文献类型：
--
作者：
Mark Weber
在这篇文章中，我们给出了一个由算子构成的多项式2-单子的构造，并描述了由此产生的2-单子的代数。这种构造不同于从算子到单体的标准构造，因为我们关联的2-单体的代数是原始算子的范畴代数。此外，它使我们能够以规范的方式将歌剧刻画为范畴多项式单体。这一观点揭示了范畴多项式单子作为歌剧、猫剧和俱乐部的统一环境。我们用2-范畴的方法从相应的2-单子中恢复了单子的标准构造，并将两者的代数理解为范畴的猫-算子的弱态射。一般对称么半群范畴内的算子代数以一种规范的方式由我们的新的伴随2-单子产生。当算子是sigma自由的时，我们建立了关于Lack发现的2-Monad的代数上的模型结构的Quillen等价，在我们相关的2-Monad的严格代数和标准2-Monad的严格代数之间。
In this article we give a construction of a polynomial 2-monad from an operad and describe the algebras of the 2-monads which then arise. This construction is dierent from the standard construction of a monad from an operad in that the algebras of our associated 2-monad are the categoried algebras of the original operad. Moreover it enables us to characterise operads as categorical polynomial monads in a canonical way. This point of view reveals categorical polynomial monads as a unifying environment for operads, Cat-operads and clubs. We recover the standard construction of a monad from an operad in a 2-categorical way from our associated 2-monad as a coidentier of 2-monads, and understand the algebras of both as weak morphisms of operads into a Cat-operad of categories. Algebras of operads within general symmetric monoidal categories arise from our new associated 2-monad in a canonical way. When the operad is sigma-free, we establish a Quillen equivalence, with respect to the model structures on algebras of 2-monads found by Lack, between the strict algebras of our associated 2-monad, and those of the standard one.