Quadratic Modules of Groupoids and Related Structures

Abstract

In this paper, we define functors between quadratic modules of groupoids and related structures.
The focus of this paper is on the study of functors between quadratic modules of groupoids and related
structures. Specifically, we explore the categorical equivalence between nil(2)-modules, quadratic modules,
and 2-quadratic modules over groupoids. We also define functors that relate these different types of
modules over groupoids, and investigate the categorical equivalence between them. We show that there
exists functors between the categories of 2-quadratic modules of groups and nil(2)-modules, quadratic
modules over group(oid)s.