Functoriality of the center of an algebra

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• 作者：Alexei Davydov^a ; ^{davydov@ohio.edu" class="auth_mail" title="E-mail the corresponding author} ; Liang Kong^b ; ^c ; ^{kong.fan.liang@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Ingo Runkel^d ; ^{ingo.runkel@uni-hamburg.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Monoidal categories ; Module categories ; Module functors ; Full center ; 2-functor ; Cospans ; Rational conformal field theories
• 刊名：Advances in Mathematics
• 出版年：2015
• 出版时间：5 November 2015
• 年：2015
• 卷：285
• 期：Complete
• 页码：811-876
• 全文大小：1122 K

文摘

The notion of the center of an algebra over a field k has a far reaching generalization to algebras in monoidal categories. The center then lives in the monoidal center of the original category. In this paper, we study functorial properties of the center. We show that it gives rise to a 2-functor from the bicategory of semisimple indecomposable module categories over a fusion category to the bicategory of commutative algebras in the monoidal center of this fusion category. Morphism spaces of the latter bicategory are extended from algebra homomorphisms to certain categories of cospans. We conjecture that the above 2-functor arises from a lax 3-functor between tricategories, and that in this setting one can relax the conditions from fusion categories to finite tensor categories. Our construction is motivated by two-dimensional conformal field theory enriched by defects of all codimensions.