Introduce the definition of a spectral sequence and the construction of a spectral sequence from filtered objects. Define the décalage functor as the realization of the Whitehead tower of the filtered object and the décalage construction of the spectral sequence. Recall Lurie's definition of a spectral sequence.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/kleineat25