Comparison of spectral sequences involving bifunctors

Details Comparison of spectral sequences involving bifunctors Comparison of spectral sequences involving bifunctors

2006-10-15

arxiv.org/abs/math/0610457v5

Mathematics

K-Theory and Homology

Typos in Secs. 8.1, 8.2 corrected. Appeared in Documenta Math. 13, 677-737, 2008

Scientific paper

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".

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