Year: 2005
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Tsemo, Aristide
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1552268064