= Cohomological Serre spectral sequence
{title2=$E_2^{p,q}=H^p(B;H^q(F;A))\Rightarrow H^{p+q}(E;A)$}
For a <Serre fibration>, this first-quadrant spectral sequence has differential of bidegree $(r,1-r)$ and a fiber-cohomology local coefficient system on the base. A <simply connected> base makes that system constant. Its edge map is restriction to the fiber; a surviving fiber class is the restriction of a total-space class. For commutative ring coefficients it is multiplicative and its differentials are graded derivations.
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