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# Homology, Homotopy and Applications

## Volume 18 (2016)

### Number 1

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

Pages: 71 – 98

DOI: http://dx.doi.org/10.4310/HHA.2016.v18.n1.a5

#### Author

#### Abstract

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