Prelinear Hilbert algebras

TL;DR

This paper explicitly describes the left adjoint of a functor between G"odel algebras and prelinear Hilbert algebras, and explores coproducts in the latter category.

Contribution

It provides a detailed construction of the left adjoint functor and investigates coproducts of finite prelinear Hilbert algebras.

Findings

Explicit description of the left adjoint functor.

Characterization of coproducts of finite algebras.

Enhanced understanding of algebraic relationships in prelinear Hilbert algebras.

Abstract

In this paper we give an explicit description of the left adjoint of the forgetful functor from the algebraic category of G\"odel algebras (i.e., prelinear Heyting algebras) to the algebraic category of bounded prelinear Hilbert algebras. We apply this result in order to study possible descriptions of the coproduct of two finite algebras in the algebraic category of prelinear Hilbert algebras.