Distributive laws and Koszulness
Annales de l'Institut Fourier, Volume 46 (1996) no. 2, pp. 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.

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

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