Introduction to Homological Algebra
January - March 2012. Dr. K. Erdmann.
This is a basic introduction, with examples motivated by representation
theory, of groups, and of finite-dimensional algebras.
Topics:
- The language of categories and functors.
- Sums, products, exact sequences.
- Adjoints.
- Pull-back and pushout; direct and inverse limits.
- Projective and injective modules, flat modules.
- Chain complexes, homology functors.
- Ext and Tor. Cohomology rings.
- Triangulated categories.
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