Quadratic modules of groupoids and related structures

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 existence of functors 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 functors exist between the categories of 2-quadratic modules of groups, nil(2)-modules, and quadratic modules over group(oid)s.