标题： 同伦方法到模的张量积 显示英文标题

标题： Homotopical Approach to Tensor Products of Modules

摘要： 范畴论提供了一种方法，通过这种方法，许多数学的广泛领域可以通过它们相似的结构相互关联。 在Robinson的一篇论文[2]中，范畴视角提供的这种互联性使得扭积可以被实现为一个拓扑空间的同伦群，该拓扑空间正是为此目的而构建的。 然而，即使正式陈述这个结果也需要大量的代数、拓扑和范畴论的预备知识。 本文档的目标是提供一个自包含的指南，介绍进行此类数学工作所需的基本概念和结果，仅包含少量证明，旨在使同伦代数领域更加易懂。 我们仅假设读者熟悉拓扑空间和群，因此适合本科生阅读。 该项目最终讨论了上述Robinson的结果，并进行了一项计算作为概念验证。 显示英文摘要

摘要： 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.