From $L_{\infty }$ algebroids to $L_{\infty }$ spaces: Part I

Abstract

The notion of $L_{\infty }$ spaces over dg manifolds is developed. An equivalence between the category of transitive $L_{\infty }$ algebroids and that of $L_{\infty }$ spaces is established, and this equivalence detects weak equivalences. Moreover, a faithful functor from $L_{\infty }$ algebroids to $L_{\infty }$ spaces is constructed, which also detects weak equivalences.

arXiv comment46 pages