Homotopy models for $L_{\infty }[1]$-algebras in higher degrees

Abstract

We propose a model of higher homotopy theory of $L_{\infty }[1]$-morphisms as a natural generalization of the $A_{\infty }$-homotopies defined by Fukaya-Oh-Ohta-Ono \cite{FOOO1}. Within this framework, we show that a filling condition holds for simplices whose vertices are assigned quasi-isomorphisms.

arXiv comment22 pages. A reformatted version as an independent preprint from arXiv:2511.05206v1, focusing on Part I (Homological Algebra)