Distributive laws and Koszulness
Annales de l'Institut Fourier, Volume 46 (1996) no. 2, p. 307-323

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.

Une loi distributive est une façon de composer deux structures algébriques, disons $𝒰$ et $𝒱$, en une structure algébrique plus complexe $𝒲$. Le but de ce travail est de comprendre les lois distributives en termes d’opérades. Le résultat central dit que si les opérades correspondant à $𝒰$ et $𝒱$ sont de Koszul, alors l’opérade correspondant à $𝒲$ est aussi de Koszul. On donne une application à la cohomologie des espaces de configurations.

@article{AIF_1996__46_2_307_0,
author = {Markl, Martin},
title = {Distributive laws and Koszulness},
journal = {Annales de l'Institut Fourier},
publisher = {Association des Annales de l'institut Fourier},
volume = {46},
number = {2},
year = {1996},
pages = {307-323},
doi = {10.5802/aif.1516},
zbl = {0853.18005},
mrnumber = {97i:18008},
language = {en},
url = {http://www.numdam.org/item/AIF_1996__46_2_307_0}
}

Markl, Martin. Distributive laws and Koszulness. Annales de l'Institut Fourier, Volume 46 (1996) no. 2, pp. 307-323. doi : 10.5802/aif.1516. http://www.numdam.org/item/AIF_1996__46_2_307_0/

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