Erratum to "$B_2$-crystals: Axioms, structure, models" [J. Combin. Theory, Ser. A, 116 (2009), 265--289]

TL;DR

This erratum clarifies and corrects the implementation of axioms for finite B2-crystals, providing a local characterization and fixing inaccuracies from the original 2009 paper.

Contribution

It introduces a purely local characterization for finite B2-crystals and corrects previous inaccuracies in the axioms and implementation details.

Findings

Provides a local axiomatic framework for B2-crystals

Corrects inaccuracies in the original axioms

Enhances understanding of B2-crystal structure

Abstract

In this erratum we explain how to implement some axioms stated in our paper of 2009 so as to obtain a purely "local" characterization for finite $B_2$-crystals, which was declared but not clarified at some moments there. Also we correct some inaccuracies in that paper.