论文标题
Unital Operad，Monoid，Monad和Bar构造
Unital operads, monoids, monads, and bar constructions
论文作者
论文摘要
我们将对称单体类别中的Unital Operad描述为单型$λ$序列的单体类别中的单体。这是凯利（Kelly）对对称序列单体类别中的旧作战描述的新变体。与Unital Operad相关的单子是迭代环空间理论和分解同源性的感兴趣，以及许多其他应用。我们对Unital Operads的新描述允许在此类应用中使用的双面元中杆构建体与“经典”单型单侧杆构建体之间进行启发性比较。它还允许对扫描图在分解同源性中的非亚洲庞加莱二元性中心进行更概念性的理解。
We give a description of unital operads in a symmetric monoidal category as monoids in a monoidal category of unital $Λ$-sequences. This is a new variant of Kelly's old description of operads as monoids in the monoidal category of symmetric sequences. The monads associated to unital operads are the ones of interest in iterated loop space theory and factorization homology, among many other applications. Our new description of unital operads allows an illuminating comparison between the two-sided monadic bar constructions used in such applications and "classical" monoidal two-sided bar constructions. It also allows a more conceptual understanding of the scanning map central to non-abelian Poincaré duality in factorization homology.
