超、量子和非对易物种
Super, quantum and non-commutative species
摘要：
我们介绍了一种方法的范畴环，通过分配范畴的概念与负对象，并用它来奠定了范畴的基础，研究超，量子和非交换组合。通过代数和几何之间的对偶性，这些构造为各种类型的仿射空间提供了一种新的构造方法，因此我们的工作可以被看作是范畴几何构造的一个起点。
英文摘要：
We introduce an approach to the categorification of rings, via the notion of distributive categories with negative objects, and use it to lay down categorical foundations for the study of super, quantum and non-commutative combinatorics. Via the usual duality between algebra and geometry, these constructions provide categorifications for various types of affine spaces, thus our works may be regarded as a starting point towards the construction of a categorical geometry.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
