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arXiv 2201.095512022-01math.CT

将拓扑斯的语言表示为 span 范畴的商

Representing the language of a topos as quotient of the category of spans

M. Golshani, A. Shiralinasab Langari

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AI总结：

本文通过 span 范畴的商刻画拓扑斯语言，并分析由逻辑关系诱导的商，进而证明以逻辑函子为态射时 Boolean 拓扑斯范畴构成拓扑斯范畴的反射子范畴。

摘要：

我们利用 span 范畴的商来引入拓扑斯的语言。我们还研究逻辑关系以及由这些逻辑关系导出的 span 范畴的商。作为应用，我们证明：当态射为逻辑函子时，Boolean 拓扑斯范畴是拓扑斯范畴的一个反射子范畴。

英文摘要：

We use quotients of span categories to introduce the language of a topos. We also study the logical relations and the quotients of span categories derived from them. As an application we show that the category of Boolean toposes is a reflective subcategory of the category of toposes, when the morphisms are logical functors.

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