Logarithmic tensor category theory, III: Intertwining maps and tensor product bifunctors

TL;DR

This paper develops a general tensor category theory for vertex operator algebra modules, focusing on intertwining maps and tensor product bifunctors to enhance the understanding of module interactions.

Contribution

It introduces and studies intertwining maps and tensor product bifunctors within the framework of tensor category theory for vertex operator algebra modules.

Findings

Established a framework for intertwining maps in tensor categories

Defined and analyzed tensor product bifunctors for module categories

Advanced the theoretical foundation for tensor categories in vertex algebra

Abstract

This is the third part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part III), we introduce and study intertwining maps and tensor product bifunctors.