(also nonabelian homological algebra)
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For
a filtered object in an abelian category , the associated graded object is the graded object which in degree is the cokernel of the th inclusion, fitting into a short exact sequence
hence the quotient of the th layer of by the next lower one:
For an abelian category and a double complex in , let be the corresponding total complex. This is naturally filtered by either row-degree or by column-degree. The corresponding associated graded complex is what the terms in the spectral sequence of a filtered complex compute.
Discussion of the universal property of the associated graded construction on mathoverflow
Last revised on November 25, 2019 at 14:34:08. See the history of this page for a list of all contributions to it.