2006/10/15 by Matthias Kuenzer, Kuenzer, Matthias
Mathematics · Physics and Astronomy · #18G40 #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.math/0610457
openalex publication_date 2006/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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, E1-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".