Multiplicative Structures of 2-dimensional Topological Quantum Field Theory (2003)
BibTeX
@MISC{Moskaliuk03multiplicativestructures,
author = {S. S. Moskaliuk and A. T. Vlassov},
title = {Multiplicative Structures of 2-dimensional Topological Quantum Field Theory },
year = {2003}
}
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Abstract
Category theory provides a uniform method of encoding mathematical structures and universal constructions with them. In this article we apply the method of additional structures on the objects of a category to deform a comonoid structure, used implicitly in all categories. To deform this comultiplication we consider internal categories in a monoidal category with some special properties. Then we consider structures over comonoids and show that deformed internal categories form a 2-category. This provides the possibility to study, in a uniform way, different types of generalized multiplicative and comultiplicative structures of 2-dimensional Topological Quantum Field Theory.
