74 citations · 252 across the 24 of their papers we have counts for
28 papers
Homotopy theories via the magnitude-path spectral sequence
Muriel Livernet, Emily Roff, Sarah Whitehouse
We introduce a family of homotopy theories for generalized metric spaces with natural number distances, via the magnitude-path spectral sequence (MPSS). The first page of the MPSS…
Model category structures on truncated multicomplexes for complex geometry
Joana Cirici, Muriel Livernet, Sarah Whitehouse
To a bicomplex one can associate two natural filtrations, the column and row filtrations, and then two associated spectral sequences. This can be generalized to -multicomplexes.…
Spectral sequences via linear presheaves
Muriel Livernet, Sarah Whitehouse
We study homotopy theory of the category of spectral sequences with respect to the class of weak equivalences given by maps which are quasi-isomorphisms on a fixed page. We introdu…
Rigidification of cubical quasi-categories
Pierre-Louis Curien, Muriel Livernet, Gabriel Saadia
We construct a cubical analogue of the rigidification functor from quasi-categories to simplicial categories present in the work of Joyal and Lurie. We define a functor from the ca…
Homotopy theory of spectral sequences
Muriel Livernet, Sarah Whitehouse
Let be a commutative ring with unit. We consider the homotopy theory of the category of spectral sequences of -modules with the class of weak equivalences given by those mor…
Model category structures on multicomplexes
Xin Fu, Ai Guan, Muriel Livernet +1
We present a family of model structures on the category of multicomplexes. There is a cofibrantly generated model structure in which the weak equivalences are the morphisms inducin…