Homological Algebra: Basics and Applications

This lecture introduces the fundamental concepts of Homological algebra, which serves as a crucial tool in various algebra-related research areas such as topology, algebraic geometry, and group theory. The lecture covers the definition and significance of Ext modules, which are essential for understanding different (co-)homology theories used in modern mathematics. Through examples and explanations, students will grasp the importance of Homological algebra in defining and utilizing various (co-)homology theories in different mathematical fields.