Naturality of the $\infty$-Categorical Enriched Yoneda Embedding

Shay Ben-Moshe

doi:10.1016/j.jpaa.2024.107625

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arXiv · 2301.00601

Naturality of the $\infty$-Categorical Enriched Yoneda Embedding

Shay Ben-Moshe

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Abstract

We make Hinich's $\infty$-categorical enriched Yoneda embedding natural. To do so, we exhibit it as the unit of a partial adjunction between the functor taking enriched presheaves and Heine's functor taking a tensored category to an enriched category. Furthermore, we study a finiteness condition of objects in a tensored category called being atomic, and show that the partial adjunction restricts to a (non-partial) adjunction between taking enriched presheaves and taking atomic objects.

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Shay Ben-Moshe. 2023-01-02. Naturality of the $\infty$-Categorical Enriched Yoneda Embedding. https://doi.org/10.1016/j.jpaa.2024.107625

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