Naturality of the $\infty$-Categorical Enriched Yoneda Embedding
Category Theory
2024-07-09 v4 Algebraic Topology
Abstract
We make Hinich's -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.
Keywords
Cite
@article{arxiv.2301.00601,
title = {Naturality of the $\infty$-Categorical Enriched Yoneda Embedding},
author = {Shay Ben-Moshe},
journal= {arXiv preprint arXiv:2301.00601},
year = {2024}
}
Comments
v3: published version, 26 pages. v4: added subsection 4.0 on left adjoints in 2-categories correcting a slight oversight, 28 pages