Martin, what gave you idea that cochain complex is obtained
by inverting matrices? Chain complex requires that product
of two consequtive matrices is 0, so normally matrices
are noninvertible (some may be invertible, but this is an
exception).
You could obtain cochain complex by transposing matrices,
or more generally applying HOM functor with fixed second
argument, but that is not the only way to produce
cochain complexes.
--
Waldek Hebisch
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