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We describe a conjecture on the algebra of higher cohomology operations whichleads to the computations of the differentials in the Adams spectral sequence.For this we introduce the notion of an n-th order track category which issuitable to study higher order Toda brackets and the differentials in spectralsequences. We describe various examples of higher order track categories whichare topological, in particular the track category of higher cohomologyoperations. Also differential algebras give rise to higher order trackcategories.

Higher order track categories and the algebra of higher order cohomology operations