Distributeurs et théorie de la forme
Distributive law is a way to compose two algebraic structures, say and , into a more complex algebraic structure . The aim of this paper is to understand distributive laws in terms of operads. The central result says that if the operads corresponding respectively to and are Koszul, then the operad corresponding to is Koszul as well. An application to the cohomology of configuration spaces is given.
We investigate the triples in the category of compacta whose functorial parts are normal functors in the sense of E.V. Shchepin (normal triples). The problem of lifting of functors to the categories of algebras of the normal triples is considered. The distributive law for normal triples is completely described.
It is shown that the construct of supertopological spaces and continuous maps is topological.
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...