(also nonabelian homological algebra)
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An unbounded chain complex
is called connective if it has no nontrivial homology groups in negative degree. Often one means more strictly that it is connective if it is concentrated in non-negative degree, hence if for all , hence if it is of the form
Such connective chain complexes are the connective objects in the -category of chain complexes. Rearding under the stable Dold-Kan correspondence as -module spectra they are the connective spectra.
Hence a connective chain complex is in particular a bounded chain complex, bounded from below.
The Dold-Kan correspondence asserts that connective chain complexes of abelian groups are equivalent to abelian simplicial groups.
Last revised on April 20, 2023 at 07:25:43. See the history of this page for a list of all contributions to it.