kernel f
ker f
The kernel of a chain complex map $f : C \to D$ is the complex $E$ whose $i-th$ term is $kernel(f_i)$, and whose differential is induced from the differential on the source.
In the following example, we first construct a random complex morphism $f : C \to D$. We consider the exact sequence $0 \to D \to cone(f) \to C[-1] \to 0$. For the maps $g : D \to cone(f)$ and $h : cone(f) \to C[-1]$, we compute the kernel.
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There is a canonical map of complexes from the kernel to the source.
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The source of this document is in Complexes/ChainComplexMapDoc.m2:2406:0.