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chain homotopy equivalence
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(Definition)
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Let $C$ and $D$ be two objects from the abelian category of chain complexes. A morphism (or chain map) $f\colon C\to D$ is said to be a chain homotopy equivalence if there is a morphism $g\colon D\to C$ such that
- there is a chain homotopy between $fg$ and $1\colon D\to D$ and
- there is a chain homotopy between $gf$ and $1\colon C\to C$
If a chain homotopy equivalence from a chain complex $C$ to $D$ exists, then $C$ is said to be chain homotopy equivalent to $D$ Chain homotopy equivalence is an equivalence relation among chain complexes.
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"chain homotopy equivalence" is owned by CWoo.
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Cross-references: equivalence relation, chain homotopy, chain map, morphism, chain complexes, abelian category, objects
There are 3 references to this entry.
This is version 3 of chain homotopy equivalence, born on 2004-11-24, modified 2004-11-24.
Object id is 6525, canonical name is ChainHomotopyEquivalence.
Accessed 3508 times total.
Classification:
| AMS MSC: | 18G35 (Category theory; homological algebra :: Homological algebra :: Chain complexes) |
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Pending Errata and Addenda
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