Hermitian Categories, extension of scalars and systems of hermitian forms

TL;DR

This paper develops a Witt group framework for sesquilinear forms in hermitian categories, extends scalar operations for hermitian categories over fields, and generalizes results to systems of forms, advancing algebraic understanding.

Contribution

It introduces a Witt group for sesquilinear forms in hermitian categories and extends scalar and form system results to broader algebraic contexts.

Findings

Defined a Witt group for sesquilinear forms in hermitian categories

Extended scalar operations for hermitian categories over fields of characteristic not 2

Generalized results to systems of sesquilinear 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.