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Distributive laws and Koszulness

Martin Markl (1996)

Annales de l'institut Fourier

Distributive law is a way to compose two algebraic structures, say 𝒰 and 𝒱 , into a more complex algebraic structure 𝒲 . 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 𝒰 and 𝒱 are Koszul, then the operad corresponding to 𝒲 is Koszul as well. An application to the cohomology of configuration spaces is given.

Distributivity law for the normal triples in the category of compacta and lifting of functors to the categories of algebras

Michael M. Zarichnyi (1991)

Commentationes Mathematicae Universitatis Carolinae

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.

Double clubs

Richard Garner (2006)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Double complexes and vanishing of Novikov cohomology

Hüttemann, Thomas (2011)

Serdica Mathematical Journal

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...

Double vector spaces

Alena Vanžurová (1987)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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