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

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.

v3: published version, 26 pages. v4: added subsection 4.0 on left adjoints in 2-categories correcting a slight oversight, 28 pages

References in corpus (1)

• Higher Semiadditive Algebraic K-Theory and Redshift

Cited by in corpus (1)

• Higher Semiadditive Algebraic K-Theory and Redshift