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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.

Equivariant Cohomology and Stable Cohomotopy.

Czes Kosniowski (1974)

Mathematische Annalen

Equivariant Homology and Mackey Functors.

Tammo tom Dieck (1973)

Mathematische Annalen

Exactitude à gauche du foncteur $H_{b}^{n} (-, 𝐑)$ de cohomologie bornée réelle

Abdesselam Bouarich (2001)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Extension of topological homology theories to partially orderd sets.

Gudrun Kalmbach (1976)

Journal für die reine und angewandte Mathematik

Extensions of super Lie algebras.

Alekseevsky, Dmitri, Michor, Peter W., Ruppert, W.A.F. (2005)

Journal of Lie Theory

Factorization systems for symmetric cat-groups.

Kasangian, S., Vitale, E.M. (2000)

Theory and Applications of Categories [electronic only]

Forms and mappings. I: Generalities

Andrzej Prószyński (1984)

Fundamenta Mathematicae

Galois theory and double central extensions.

Gran, Marino, Rossi, Valentina (2004)

Homology, Homotopy and Applications

G-functors, G-posets and homotopy decompositions of G-spaces

Stefan Jackowski, Jolanta Słomińska (2001)

Fundamenta Mathematicae

We describe a unifying approach to a variety of homotopy decompositions of classifying spaces, mainly of finite groups. For a group G acting on a poset W and an isotropy presheaf d:W → (G) we construct a natural G-map $h o c o l i m_{_{d}} G / d (-) \to | W |$ which is a (non-equivariant) homotopy equivalence, hence $h o c o l i m_{_{d}} E G \times_{G} F_{d} \to E G \times_{G} | W |$ is a homotopy equivalence. Different choices of G-posets and isotropy presheaves on them lead to homotopy decompositions of classifying spaces. We analyze higher limits over the categories associated to isotropy presheaves...

Homological algebra and divergent series.

Gorbounov, Vassily, Schechtman, Vadim (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Homological perturbation theory and associativity.

Real, Pedro (2000)

Homology, Homotopy and Applications

Homology of $n$ -fold groupoids.

Everaert, Tomas, Gran, Marino (2010)

Theory and Applications of Categories [electronic only]

Homology theory in the alternative set theory I. Algebraic preliminaries

Jaroslav Guričan (1991)

Commentationes Mathematicae Universitatis Carolinae

The notion of free group is defined, a relatively wide collection of groups which enable infinite set summation (called commutative $π$ -group), is introduced. Commutative $π$ -groups are studied from the set-theoretical point of view and from the point of view of free groups. Commutativity of the operator which is a special kind of inverse limit and factorization, is proved. Tensor product is defined, commutativity of direct product (also a free group construction and tensor product) with the special...

Intertwining operators over L1 (G) for G ? [PG] ? [SIN].

Volker Runde (1996)

Mathematische Zeitschrift

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