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arXiv 2001.114772020-01-30math.CT

离散2-纤维化

Discrete 2-Fibrations

Michael Lambert

备注：: 43 pages
发表信息：: In: Higher Structures 8(1), May 2024, pp. 54-96

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AI总结：

该研究提出离散2-纤维化的定义，证明其通过2-等价对应特定范畴值2-函子，最终目标是证其在范畴2-范畴切片上具有2-单子性，是普通离散纤维化的二维类比拓展。

摘要：

本文旨在构建普通离散纤维化概念的二维类比。我们提出了离散2-纤维化的定义，并证明这类离散2-纤维化通过2-等价对应于某类取值于范畴的2-函子。本文的最终目标是证明离散2-纤维化在范畴2-范畴的一个切片上是2-单子性的。

英文摘要：

This paper is concerned with developing a 2-dimensional analogue of the notion of an ordinary discrete fibration. A definition is proposed, and it is shown that such discrete 2-fibrations correspond via a 2-equivalence to certain category-valued 2-functors. The ultimate goal of the paper is to show that discrete 2-fibrations are 2-monadic over a slice of the 2-category of categories.

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