Hermitian Categories, extension of scalars and systems of hermitian forms

Abstract

In this paper we define a notion of Witt group for sesquilinear forms in hermitian categories, which in turn provides a notion of Witt group for sesquilinear forms over rings with involution. We also study the extension of scalars for K-linear hermitian categories, where K is a field of characteristic not 2. We finally extend several results concerning sesquilinear forms to the setting of systems of such forms.