论文标题
Plethysm产品，元素和加上构造
Plethysm Products, Element and Plus Constructions
论文作者
论文摘要
通过将类别视为双模型的同构群体，我们在三个层面上构建了称为Plethysm产物的单模型，即三个级别：对于双模型，相对双模型和可分子化的双模型。对于双模型，我们按类别的一般行动设置工作。我们提供了一个全面的理论，将这些水平彼此联系起来，并提供了元素元素构造，索引富集，装饰和代数。 专门从事类固醇动作会导致申请，包括加大构造。在这种情况下，第三级涵盖了Baez-Dolan及其概括的已知结构，正如我们所证明的那样。一个新的结果是，加上构造也可以实现与我们定义的单体结构兼容的元素构建。这使我们能够证明元素和加上构造之间的交通便利性，其特殊情况较早宣布。在第三级上专业的结果会产生标准，当可以将类似于Operad的结构定义为多包肌（由Oprads的体现）时。
Motivated by viewing categories as bimodule monoids over their isomorphism groupoids, we construct monoidal structures called plethysm products on three levels: that is for bimodules, relative bimodules and factorizable bimodules. For the bimodules, we work in the general setting of actions by categories. We give a comprehensive theory linking these levels to each other as well as to Grothendieck element constructions, indexed enrichments, decorations and algebras. Specializing to groupoid actions leads to applications including the plus construction. In this setting, the third level encompasses the known constructions of Baez-Dolan and its generalizations, as we prove. One new result is that that the plus construction can also be realized an element construction compatible with monoidal structures that we define. This allows us to prove a commutativity between element and plus constructions a special case of which was announced earlier. Specializing the results on the third level yield a criterion, when a definition of operad-like structure as a plethysm monoid -- as exemplified by operads -- is possible.
