A Beginner’s Guide to Homological Algebra: A Comprehensive Introduction for Students

作     者：Eskenazi, Andy You, Kevin Vauclain, Will Murugadoss, Robin 

作者机构：Department of Mathematics University of Pennsylvania United States Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania United States Department of Computer and Information Science University of Pennsylvania United States 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2022年

核心收录：

主　　题：Algebra 

摘      要：Homological algebra is often understood as the translator between the world of topology and algebra. However, this branch of mathematics is worth studying by itself, given that it provides fascinating perspectives about other disciplines, most notably, category theory. In this paper, we seek to provide an introductory guide for advanced students of mathematics and related specialties seeking to get started on homological algebra, covering the necessary central topics to later delve deeper into more complex aspects of this field and beyond. This work starts by presenting the notion of chain complexes of algebraic structures, and then moves into exploring homology modules and chain homotopies. Next, we provide an overview of projective resolutions and conclude by entering the world of category theory by looking at Tor functors. © 2022, CC BY.