Auslander's defect formula and a commutative triangle in an exact category

TL;DR

This paper proves Auslander's defect formula within an exact category and constructs a commutative triangle linking Auslander bijections with generalized Auslander-Reiten duality.

Contribution

It introduces a new proof of Auslander's defect formula and establishes a novel connection between Auslander bijections and duality in exact categories.

Findings

Proved Auslander's defect formula in an exact category

Constructed a commutative triangle involving Auslander bijections and duality

Enhanced understanding of the relationship between these concepts

Abstract

We prove Auslander's defect formula in an exact category, and obtain a commutative triangle involving the Auslander bijections and the generalized Auslander-Reiten duality.