Suppose given functors A x A' -F-> B -G-> C between abelian categories, an
object X in A and an object X' in A' such that certain conditions hold. We show
that, E_1-terms exempt, the Grothendieck spectral sequence of the composition
of F(X,-) and G evaluated at X' is isomorphic to the Grothendieck spectral
sequence of the composition of F(-,X') and G evaluated at X. So instead of
"resolving X' twice", we may just as well "resolve X twice".Comment: Typos in Secs. 8.1, 8.2 corrected. Appeared in Documenta Math. 13,
677-737, 200
