  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.
