# Linkage of modules by reflexive morphisms

## TL;DR

This paper introduces a generalized concept of module linkage via reflexive homomorphisms, extending classical results from Gorenstein to Cohen-Macaulay rings, and explores the dual notion of colinkage.

## Contribution

It unifies existing linkage theories and broadens their applicability to Cohen-Macaulay rings, establishing an equivalence between linked and colinked modules.

## Key findings

- Several Gorenstein linkage results hold over Cohen-Macaulay rings.
- Introduces the concept of colinkage and proves an adjoint equivalence.
- Generalizes module linkage theory beyond Gorenstein rings.

## Abstract

In this paper, we introduce and study the notion of linkage of modules by reflexive homomorphisms. This notion unifies and generalizes several known concepts of linkage of modules and enables us to study the theory of linkage of modules over Cohen-Macaulay rings rather than the more restrictive Gorenstein rings. It is shown that several known results for Gorenstein linkage are still true in the more general case of module linkage over Cohen-Macaulay rings. We also introduce the notion of colinkage of modules and establish an adjoint equivalence between the linked and colinked modules.