2005/05/06 by Aristide Tsemo, Tsemo, Aristide
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.CT
paper · pdf · doi:10.48550/arxiv.math/0505104
26 pages, 7 references. We define Tanakian quadratic categories
openalex publication_date 2005/05/06 · arxiv created 2005/06/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A quadratic algebra is a homogeneous algebra generated by its elements of degree 1. Manin has endowed the category of quadratic algebras with two tensor products. These structures have been adapted to operads by Ginsburg and Kapranov. Berger has defined such tensor products for n-homogeneous algebras. The purpose of this paper is to define the notion of quadratic category, which is a category endowed with two tensor products. The Manin and Ginsburg-Kapranov constructions are examples of quadratic categories. We define also a Koszul complex, n-homogeneous operads and show how this notion can be applied to study coherence relations for n-categories.