What does chain complex mean?
Definitions for chain complex
cha·in com·plex
This dictionary definitions page includes all the possible meanings, example usage and translations of the word chain complex.
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Wiktionary
chain complexnoun
A sequence of Abelian groups, together with a sequence of boundary homomorphisms
Wikipedia
Chain complex
In mathematics, a chain complex is an algebraic structure that consists of a sequence of abelian groups (or modules) and a sequence of homomorphisms between consecutive groups such that the image of each homomorphism is included in the kernel of the next. Associated to a chain complex is its homology, which describes how the images are included in the kernels. A cochain complex is similar to a chain complex, except that its homomorphisms are in the opposite direction. The homology of a cochain complex is called its cohomology. In algebraic topology, the singular chain complex of a topological space X is constructed using continuous maps from a simplex to X, and the homomorphisms of the chain complex capture how these maps restrict to the boundary of the simplex. The homology of this chain complex is called the singular homology of X, and is a commonly used invariant of a topological space. Chain complexes are studied in homological algebra, but are used in several areas of mathematics, including abstract algebra, Galois theory, differential geometry and algebraic geometry. They can be defined more generally in abelian categories.
Wikidata
Chain complex
In mathematics, chain complex and cochain complex are constructs originally used in the field of algebraic topology. They are algebraic means of representing the relationships between the cycles and boundaries in various dimensions of a topological space. More generally, homological algebra includes the study of chain complexes in the abstract, without any reference to an underlying space. In this case, chain complexes are studied axiomatically as algebraic structures. Applications of chain complexes usually define and apply their homology groups; in more abstract settings various equivalence relations are applied to complexes. Chain complexes are easily defined in abelian categories, also.
Numerology
Chaldean Numerology
The numerical value of chain complex in Chaldean Numerology is: 5
Pythagorean Numerology
The numerical value of chain complex in Pythagorean Numerology is: 6
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"chain complex." Definitions.net. STANDS4 LLC, 2024. Web. 26 Apr. 2024. <https://www.definitions.net/definition/chain+complex>.
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