# A logical and algebraic characterization of adjunctions between generalized quasi-varieties

## TL;DR

This paper provides a logical and algebraic framework to characterize right adjoint functors between generalized quasi-varieties, linking adjunctions with translations in relative equational logic, inspired by McKenzie's work.

## Contribution

It introduces a novel correspondence between adjunctions and translations in relative equational consequences for generalized quasi-varieties.

## Key findings

- Established a logical-algebraic characterization of adjunctions.
- Connected adjunctions with translations in relative equational logic.
- Extended McKenzie's ideas to a broader class of categories.

## Abstract

We present a logical and algebraic description of right adjoint functors between generalized quasi-varieties, inspired by the work of McKenzie on category equivalence. This result is achieved by developing a correspondence between the concept of adjunction and a new notion of translation between relative equational consequences.