Higher Toda brackets and the Adams spectral sequence in triangulated categories

@article{Christensen2015HigherTB,
  title={Higher Toda brackets and the Adams spectral sequence in triangulated categories},
  author={J. Daniel Christensen and Martin Frankland},
  journal={arXiv: Algebraic Topology},
  year={2015}
}
The Adams spectral sequence is available in any triangulated category equipped with a projective or injective class. Higher Toda brackets can also be defined in a triangulated category, as observed by B. Shipley based on J. Cohen's approach for spectra. We provide a family of definitions of higher Toda brackets, show that they are equivalent to Shipley's, and show that they are self-dual. Our main result is that the Adams differential $d_r$ in any Adams spectral sequence can be expressed as an… 
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