Calcul des satellites et présentations des bimodules à l'aide des carrés exacts (2e partie)
Cartan-Eilenberg projective, injective and flat complexes
Let be an associative ring with identity and a class of -modules. In this article: we first give a detailed treatment of Cartan-Eilenberg complexes and extend the basic properties of the class to the class ). Secondly, we study and give some equivalent characterizations of Cartan-Eilenberg projective, injective and flat complexes which are similar to projective, injective and flat modules, respectively. As applications, we characterize some classical rings in terms of these complexes,...
Categorification of the virtual braid groups
We extend Rouquier’s categorification of the braid groups by complexes of Soergel bimodules to the virtual braid groups.
Chain complexes and stable categories.
Chain Equivalences and Schanuel's Lemma.
Chain functors with isomorphic homology.
Chain homotopy pullbacks and pushouts
Cochain operations and subspace arrangements.
Coherent prohomotopical algebra
Cubical Abelian groups with connections are equivalent to chain complexes.