Algebras of Higher Operads as Enriched Categories
Algebras of Higher Operads as Enriched Categories
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作为丰富范畴的高级运算代数
DOI：
10.1007/s10485-008-9179-7
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发表时间：
2008
影响因子：
0.6
通讯作者：
Mark Weber
中科院分区：
文献类型：
--
作者：
M. Batanin;Mark Weber
高维Gray张量积的高维类似物的系统构造是高维范畴理论中的一个未决问题。在这篇文章中，我们开始使球状歌剧的机制(巴丹宁，高级数学136：39-103,1998)来适应这项任务。我们给出了任意归一化(n + 1)算子A在n球集范畴上张量积的一般构造，使得A的代数可以被重新捕获为诱导张量积的丰富范畴.这是协调更高范畴理论的整体方法和单纯方法的重要一步，因为在单纯方法中，人们按照弱(n + 1)-范畴是富含弱n-范畴的范畴的思想进行归纳。在这篇文章中，我们揭示了这种直觉是如何通过球状歌剧来表达的。
One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we begin to adapt the machinery of globular operads (Batanin, Adv Math 136:39–103, 1998) to this task. We present a general construction of a tensor product on the category of n-globular sets from any normalised (n + 1)-operad A, in such a way that the algebras for A may be recaptured as enriched categories for the induced tensor product. This is an important step in reconciling the globular and simplicial approaches to higher category theory, because in the simplicial approaches one proceeds inductively following the idea that a weak (n + 1)-category is something like a category enriched in weak n-categories. In this paper we reveal how such an intuition may be formulated in terms of globular operads.