On functors between categories of modules over trusses

TL;DR

This paper explores the categorical structure of modules over trusses, defining tensor products, and establishing foundational theorems like Eilenberg-Watts and Morita equivalence within this context.

Contribution

It introduces the tensor product of modules over trusses and extends key categorical theorems to this new setting, providing a foundation for further research.

Findings

Bimodules over trusses form a monoidal category

Tensor product of modules over trusses is well-defined

Truss versions of Eilenberg-Watts and Morita theorems are established

Abstract

Categorical aspects of the theory of modules over trusses are studied. Tensor product of modules over trusses is defined and its existence established. In particular, it is shown that bimodules over trusses form a monoidal category. Truss versions of the Eilenberg-Watts theorem and Morita equivalence are formulated. Projective and small-projective modules over trusses are defined and their properties studied.