Connecting homomorphism in nonabelian Cech cohomology

Hi all,

Let A, B and C sheaves of groups on a manifold X, such that A is
abelian and B and C are not abelian, and such that one has an exact
sequence
1 -> A -> B -> C -> 1, where i:A -> B.
This sequence induces the sequence in cohomology until H^1(X,C). Now,
since A is abelian, H^2(X,A) is defined, but does this implies that the
sequence in cohomology continues one step further, to H^2(X,A)?
Shouldn't we impose the condition that i(A) is a subset of Z(B), the
centre of B?

Thank you in advance,
A. Gama

.

Relevant Pages

  • Re: Number of abelian groups + exact sequence
    ... galathaea wrote: ... when A is supposed to be abelian? ... can forget about cohomology and semi-direct products. ... which is what everyone seems to be telling eugene to do ...
    (sci.math)
  • Re: Number of abelian groups + exact sequence
    ... galathaea wrote: ... when A is supposed to be abelian? ... can forget about cohomology and semi-direct products. ... of using baer sums in such calculations ...
    (sci.math)