摘要翻译：
通过点的函子的使用，我们用完全范畴的术语重新表述了超代数和超几何。这种方法增加的抽象性得到了许多巨大的优势。首先，我们证明了一个人可以完全自然地将超几何推广到无限维的上下文。其次，超几何学中一些微妙的、有时看似晦涩的观点，如Berezin-Leites-Kostant和de Witt-Rogers方法之间的关系，以及超几何学中奇数参数的精确几何意义，都在这些结果中变得清晰起来。此外，该方法还允许我们以一种简单的方式构造超对象之间的态射超空间，即与此类态射集合相关联的内Hom对象。我们的工作结果在很大程度上依赖于V.Molotkov的思想，并受到其启发，他首先概述了这里广泛阐述的方法。
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英文标题：
《A Categorical Formulation of Superalgebra and Supergeometry》
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作者：
Christoph Sachse
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Physics        物理学
二级分类：Mathematical Physics        数学物理
分类描述：Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Mathematics        数学
二级分类：Differential Geometry        微分几何
分类描述：Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis
复形，接触，黎曼，伪黎曼和Finsler几何，相对论，规范理论，整体分析
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一级分类：Mathematics        数学
二级分类：Mathematical Physics        数学物理
分类描述：math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
math.mp是math-ph的别名。这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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英文摘要：
  We reformulate superalgebra and supergeometry in completely categorical terms by a consequent use of the functor of points. The increased abstraction of this approach is rewarded by a number of great advantages. First, we show that one can extend supergeometry completely naturally to infinite-dimensional contexts. Secondly, some subtle and sometimes obscure-seeming points of supergeometry become clear in light of these results, e.g., the relation between the Berezin-Leites-Kostant and the de Witt-Rogers approaches, and the precise geometric meaning of odd parameters in supergeometry. In addition, this method allows us to construct in an easy manner superspaces of morphisms between superobjects, i.e., the inner Hom objects associated with the sets of such morphisms. The results of our work rely heavily and were inspired by the ideas of V. Molotkov, who first outlined the approach extensively expounded here.
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PDF链接：
https://arxiv.org/pdf/0802.4067