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Enriched monoidal categories I: Centers

  • Liang Kong

    Southern University of Science and Technology, Shenzhen, P. R. China; International Quantum Academy, Shenzhen, P. R. China

  • Wei Yuan

    Chinese Academy of Sciences, Beijing, P. R. China; University of Chinese Academy of Sciences, Beijing, P. R. China

  • Zhi-Hao Zhang

    University of Science and Technology of China, Hefei, Anhui Province, P. R. China; Southern University of Science and Technology, Shenzhen, Guangdong Province, P. R. China

  • Hao Zheng

    Tsinghua University, Beijing, P. R. China; Beijing Institute of Mathematical Sciences and Applications, Beijing, P. R. China; Peking University, Beijing, P. R. China; Southern University of Science and Technology, Shenzhen, Guangdong Province, P. R. China
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Abstract

This work is the first one in a series, in which we develop a mathematical theory of enriched (braided) monoidal categories and their representations. In this work, we introduce the notion of the -center (-center or -center) of an enriched (monoidal or braided monoidal) category, and compute the centers explicitly when the enriched (braided monoidal or monoidal) categories are obtained from the canonical constructions. These centers have important applications in the mathematical theory of gapless and gapped boundaries of topological phases. They also play very important roles in the higher representation theory, which is the focus of the second work in the series.

Cite this article

Liang Kong, Wei Yuan, Zhi-Hao Zhang, Hao Zheng, Enriched monoidal categories I: Centers. Quantum Topol. (2024), published online first

DOI 10.4171/QT/217