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Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology ) and abstract algebra (theory of modules and syzygies ) at the end of the 19th century, chiefly by ...
In abstract algebra, one uses homology to define derived functors, for example the Tor functors. Here one starts with some covariant additive functor F and some module X . The chain complex for X is defined as follows: first find a free module F 1 {\displaystyle F_{1}} and a surjective homomorphism p 1 : F 1 → X . {\displaystyle p_{1}:F_{1 ...
An introduction to homological algebra. Cambridge Studies in Advanced Mathematics. Vol. 38. Cambridge University Press. ISBN 978-0-521-55987-4. MR 1269324. OCLC 36131259. Yekutieli, Amnon (2019). Derived Categories. Cambridge Studies in Advanced Mathematics. Vol. 183. Cambridge University Press. ISBN 978-1108419338
Diagram chasing (also called diagrammatic search) is a method of mathematical proof used especially in homological algebra, where one establishes a property of some morphism by tracing the elements of a commutative diagram.
This is a list of homological algebra topics, by Wikipedia page. Basic techniques. Cokernel; Exact sequence; Chain complex; Differential module; Five lemma; Short ...
Homological algebra is a collection of algebraic techniques that originated in the study of algebraic topology but has also found applications to group theory and algebraic geometry The main article for this category is Homological algebra .
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