On a conceptual formulation of Haagerup’s definition of L^p-spaces of (noncommutative) von Neumann algebras:
Shigeru Yamagami, Algebraic aspects in modular theory, Publications of the Research Institute for Mathematical Sciences 28:6 (1992), 1075-1106. doi.
Shigeru Yamagami, Modular theory for bimodules, Journal of Functional Analysis 125:2 (1994), 327-357. doi.
On what came to be called Tambara-Yamagami categories:
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