A classification of degree functors, I
A remark on Koszul complexes.
Absolute homology.
Baer invariants in semi-abelian categories I: General theory.
Baer invariants in semi-abelian categories II: Homology.
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.
De Rham cohomology and homotopy Frobenius manifolds
We endow the de Rham cohomology of any Poisson or Jacobi manifold with a natural homotopy Frobenius manifold structure. This result relies on a minimal model theorem for multicomplexes and a new kind of a Hodge degeneration condition.
Double complexes and vanishing of Novikov cohomology
2010 Mathematics Subject Classification: Primary 18G35; Secondary 55U15.We consider non-standard totalisation functors for double complexes, involving left or right truncated products. We show how properties of these imply that the algebraic mapping torus of a self map h of a cochain complex of finitely presented modules has trivial negative Novikov cohomology, and has trivial positive Novikov cohomology provided h is a quasi-isomorphism. As an application we obtain a new and transparent proof that...
Effective chain complexes for twisted products
In the paper weak sufficient conditions for the reduction of the chain complex of a twisted cartesian product to a chain complex of free finitely generated abelian groups are found.
Extension categories and their homotopy
Generalized differential forms over an operand and algebraic models of fibrations. (Formes différentielles généralisées sur une opérade et modéles algébriques des fibrations.)