Bimodules and natural transformations for enriched $\infty$-categories

We introduce a notion of bimodule in the setting of enriched $\infty$-categories, and use this to construct a double $\infty$-category of enriched $\infty$-categories where the two kinds of 1-morphisms are functors and bimodules. We then consider a natural definition of natural transformations in this context, and show that in the underlying $(\infty,2)$-category of enriched $\infty$-categories with functors as 1-morphisms the 2-morphisms are given by natural transformations.

Keywords

enriched $\infty$-category, bimodule

2010 Mathematics Subject Classification

18D05, 18D20, 55U40

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Published 31 May 2016