Logarithmic tensor category theory, VII: Convergence and extension properties and applications to expansion for intertwining maps

Abstract

This is the seventh 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 VII), we give sufficient conditions for the existence of the associativity isomorphisms.

Part VII of a series of 8 papers generalizing the results in and collectively replacing arXiv:0710:2687, with new titles. 21 pages. Minor changes

References in corpus (1)

• Logarithmic tensor category theory, VIII: Braided tensor category structure on categories of generalized modules for a conformal vertex algebra

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• Representation theory of $L_k\left(\mathfrak{osp}(1|2)\right)$ from vertex tensor categories and Jacobi forms
• Tensor Categories arising from the Virasoro Algebra
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• Intertwining operators among twisted modules associated to not-necessarily-commuting automorphisms
• Representation theory of vertex operator algebras and orbifold conformal field theory