Abstract

The talk will cover homotopy theory associated with the category of spectral sequences. For each r, maps which are quasi-isomorphisms on the r page provide a class of weak equivalences. We introduce the category of extended spectral sequences and show that this is bicomplete by analysis of a certain presheaf category modelled on discs. We endow the category of extended spectral sequences with various model category structures. One of these has the property that spectral sequences is a homotopically full subcategory and so, by results of Meier, this exhibits the category of spectral sequences as a fibrant object in the Barwick-Kan  model structure on relative categories. We also note how the presheaf approach provides some insight into the décalage functor on spectral  sequences. This is joint work with Muriel Livernet.