论文标题
薄弱的$ω$ - 类别作为归纳类型的ctucads
Computads for weak $ω$-categories as an inductive type
论文作者
论文摘要
我们通过给出免费单词的明确归纳定义，对弱球状$ω$分类的Computads进行了新的描述。这产生了对Computads的新理解，并允许对$ω$ - 类别进行新的定义，从而避免了球形作业的技术。我们的框架允许通过结构诱导直接证明重要结果，我们使用它来提供新的证据，证明每一个$ω$ - 类别都等同于免费的，而具有生成器保留地图的Computads类别是Presheaf topos，是一个直接描述索引类别。我们证明，我们对$ω$ - 类别的定义与Batanin和Leinster的定义一致，并且以$ω$ - 类别的诱导的同事替代概念恰好与Garner相吻合。
We give a new description of computads for weak globular $ω$-categories by giving an explicit inductive definition of the free words. This yields a new understanding of computads, and allows a new definition of $ω$-category that avoids the technology of globular operads. Our framework permits direct proofs of important results via structural induction, and we use this to give new proofs that every $ω$-category is equivalent to a free one, and that the category of computads with generator-preserving maps is a presheaf topos, giving a direct description of the index category. We prove that our resulting definition of $ω$-category agrees with that of Batanin and Leinster and that the induced notion of cofibrant replacement for $ω$-categories coincides with that of Garner.
