Distributive laws and Koszulness
Annales de l'Institut Fourier, Tome 46 (1996) no. 2, p. 307-323
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.
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.
@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},
     mrnumber = {97i:18008},
     zbl = {0853.18005},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_1996__46_2_307_0}
}
Markl, Martin. Distributive laws and Koszulness. Annales de l'Institut Fourier, Tome 46 (1996) no. 2, pp. 307-323. doi : 10.5802/aif.1516. https://aif.centre-mersenne.org/item/AIF_1996__46_2_307_0/

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