论文标题
从定制的数学宇宙中探索数学对象
Exploring mathematical objects from custom-tailored mathematical universes
论文作者
论文摘要
座椅可以描绘成数学宇宙。除了大多数数学展开的标准纹章外，还有多种备用的替代饰面，其中数学的播放略有不同。例如，在本科生演算失败的选择公理和中间值定理中有一些座椅。这一贡献的目的是瞥见洲际景观，展示了几种特定的甲板并探索其特殊的特性，并阐明了如何提供标准托普斯通常数学对象的独特镜头。
Toposes can be pictured as mathematical universes. Besides the standard topos, in which most of mathematics unfolds, there is a colorful host of alternate toposes in which mathematics plays out slightly differently. For instance, there are toposes in which the axiom of choice and the intermediate value theorem from undergraduate calculus fail. The purpose of this contribution is to give a glimpse of the toposophic landscape, presenting several specific toposes and exploring their peculiar properties, and to explicate how toposes provide distinct lenses through which the usual mathematical objects of the standard topos can be viewed.
