Homological algebra

Homological algebra is the branch of mathematics which studies the methods of homology and cohomology in a general setting. These concepts originated in algebraic topology.

Related Topics:
Mathematics - Homology - Cohomology - Algebraic topology

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Cohomology theories have been defined for many different objects such as topological spaces, sheaves, groups, rings, Lie algebras, and C-star algebras. The study of modern algebraic geometry would be almost unthinkable without sheaf cohomology.

Related Topics:
Topological space - Sheaves - Group - Ring - Lie algebra - C-star algebra - Algebraic geometry - Sheaf cohomology

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Central to homological algebra is the notion of exact sequence; these can be used to perform actual calculations.

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A classical tool of homological algebra is that of derived functor; the most basic examples are

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Ext and Tor.

Related Topics:
Ext - Tor

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