Geodesic
Monoidal Structures on the Categories of Quadratic Data
Documenta mathematica, Tome 25 (2020), pp. 1727-1786
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The notion of 2-monoidal category used here was introduced by B. Vallette in [J. Pure Appl. Algebra 208, No. 2, 699–725 (2007; Zbl 1109.18002); Trans. Am. Math. Soc. 359, No. 10, 4865–4943 (2007; Zbl 1140.18006)] for applications in the operadic context. The starting point for this article was a remark by Yu. Manin that in the category of quadratic algebras (that is,"quantum linear spaces") one can also define 2-monoidal structure(s) with rather unusual properties. Here we give a detailed exposition of these constructions, together with their generalisations to the case of quadratic operads.
DOI : 10.4171/dm/784
Classification : 16S37, 18Mxx, 18M05, 18M50, 18M60, 18M70
Mots-clés : monoidal categories, operads, Koszul duality, 2-monoidal categories, quadratic data, black and white products 
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     author = {Yuri Ivanovich Manin and Bruno Vallette},
     title = {Monoidal {Structures} on the {Categories} of {Quadratic} {Data}},
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     volume = {25},
     doi = {10.4171/dm/784},
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Yuri Ivanovich Manin; Bruno Vallette. Monoidal Structures on the Categories of Quadratic Data. Documenta mathematica, Tome 25 (2020), pp. 1727-1786. doi: 10.4171/dm/784

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