论文标题
用于张量的模块产品的同位方法
Homotopical Approach to Tensor Products of Modules
论文作者
论文摘要
类别理论提供了一种手段，许多数学领域可以通过它们的相似结构相关。在Robinson [2]的论文中，通过分类观点提供的这种互连性允许将扭转产物作为拓扑空间的同型组实现，这本身就是为此目的而构建的。但是，即使是正式说明这一结果也需要代数，拓扑和类别理论的许多初步。 本文档的目的是为基本概念和结果提供独立的指南，几乎没有证据，需要与这种数学合作，以期使同质代数的领域更容易访问。我们只假设熟悉拓扑空间和群体，因此从本科层面可以接近。该项目最终讨论了上述鲁滨逊的结果以及计算作为概念验证的结果。
Category theory provides a means through which many far-ranging fields of mathematics can be related by their similar structure. In a paper by Robinson [2], this interconnectivity afforded by categorical perspectives allowed for the realization of torsion products as the homotopy groups of a topological space, which is itself constructed for this express purpose. However, even stating this result formally requires a multitude of preliminaries in algebra, topology, and category theory. The goal of this document is to present a self-contained guide to the fundamental concepts and results, with few proofs, required to do work with this kind of mathematics in hopes of making the field of homotopical algebra more accessible. We only assume familiarity with topological spaces and groups, so it is approachable from an undergraduate level. This project culminates in a discussion of the result of Robinson mentioned above along with a computation as a proof of concept.
