nLab
truncation of a chain complex

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Homological algebra

homological algebra

and

nonabelian homological algebra

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Definition

For C C_\bullet a chain complex, it truncation (τ C) (\tau_{\leq} C)_\bullet at some nn \in \mathbb{N} is the chain complex defined by

(τ nC) i={0 |i>n C n/B n |i=n C n |i<n, (\tau_n C)_i = \left\{ \array{ 0 & | i \gt n \\ C_n/B_n & | i = n \\ C_n & | i \lt n } \right. \,,

where B n=im(d n)B_n = im(d_n).

For connective chain complexes this is the notion of truncated object in an (infinity,1)-category realized in the (infinity,1)-category of chain complexes.

References

Created on August 24, 2012 14:13:43 by Urs Schreiber (82.113.106.22)