Department of Mathematics, University of Malta, MSD 2080 Msida, Malta
Mini Review
Homological Adventures Exploring Homological Algebra
Author(s): Soren Patwadi*
Homological algebra is a branch of mathematics that delves into the study of structures through the lens of algebraic objects called homology and
cohomology. It's a powerful tool with applications in various fields including algebraic topology, algebraic geometry, and representation theory.
In this article, we embark on a journey through the fascinating realm of homological algebra, exploring its fundamental concepts, techniques,
and applications. Homological algebra emerged from the study of algebraic topology in the early century, with pioneers like Emmy Noether
and Saunders Mac Lane laying its groundwork. Central to homological algebra are chain complexes, sequences of abelian groups or modules
connected by homomorphisms, which capture the essence of cycles, boundaries, and exact sequences. The notion of homology arises from
these complexes, providing a meas.. Read More»
DOI:
10.37421/1736-4337.2024.18.449
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