Azumaya algebras and Barr Theorem

TL;DR

This paper explores Azumaya algebras over commutative rings within a constructive framework, utilizing Barr's Theorem to establish the equivalence of two definitions via etale topology.

Contribution

It provides a constructive approach to Azumaya algebras and applies Barr's Theorem to prove the equivalence of different definitions.

Findings

Constructive treatment of etale topology and Azumaya algebras.

Proof of equivalence between two definitions of Azumaya algebra.

Application of Barr's Theorem in algebraic context.

Abstract

We study etale topology and the notion of Azumaya algebra over a commutative ring constructively. As an application of the syntactic version of Barr's Theorem, we show the equivalence between two definitions of Azumaya algebra.