English

An equivalence between two models of $\infty$-categories of enriched presheaves

Category Theory 2024-03-19 v3 Algebraic Topology

Abstract

Let OBM\mathcal{O} \to \mathrm{BM} be a BM \mathrm{BM}-operad that exhibits an \infty-category D\mathcal{D} as weakly bitensored over non-symmetric \infty-operads V,W\mathcal{V}, \mathcal{W} and C\mathcal{C} a V\mathcal{V}-enriched \infty-precategory. We construct an equivalence FunHinV(C,D)FunV(C,D)\mathrm{Fun}_{\mathrm{Hin}}^{\mathcal{V}}(\mathcal{C},\mathcal{D}) \simeq \mathrm{Fun}^{\mathcal{V}}(\mathcal{C},\mathcal{D}) of \infty-categories weakly right tensored over W\mathcal{W} between two different models of \infty-categories of V\mathcal{V}-enriched functors, one introduced by Hinich and one constructed by us.

Keywords

Cite

@article{arxiv.2306.08115,
  title  = {An equivalence between two models of $\infty$-categories of enriched presheaves},
  author = {Hadrian Heine},
  journal= {arXiv preprint arXiv:2306.08115},
  year   = {2024}
}