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

· 2015 · math.AT · arXiv 1506.07341

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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.

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math.AT 1

years

2019 1

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CONDITIONAL 1

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  • Iterated traces in 2-categories and Lefschetz theorems math.AT · 2019-08-20 · conditional · none · ref 16 · internal anchor

    Iterated traces in any 2-dualizable symmetric monoidal bicategory commute, recovering and extending a wide family of Lefschetz-type theorems.