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1. CMB Online first
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On Braided and Ribbon Unitary Fusion Categories We prove that every braiding over a unitary fusion category is
unitary and every unitary braided fusion category admits a unique
unitary ribbon structure.
Keywords:fusion categories, braided categories, modular categories Categories:20F36, 16W30, 18D10 |
2. CMB 2004 (vol 47 pp. 321)
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Classifying Spaces for Monoidal Categories Through Geometric Nerves The usual constructions of classifying spaces for monoidal categories
produce CW-complexes with
many cells that, moreover, do not have any proper geometric meaning.
However, geometric nerves of
monoidal categories are very handy simplicial sets whose simplices
have
a pleasing geometric
description: they are diagrams with the shape of the 2-skeleton of
oriented standard simplices. The
purpose of this paper is to prove that geometric realizations of
geometric nerves are classifying
spaces for monoidal categories.
Keywords:monoidal category, pseudo-simplicial category,, simplicial set, classifying space, homotopy type Categories:18D10, 18G30, 55P15, 55P35, 55U40 |