Faonte, Giovanni

Simplicial nerve of an $\cAl a_\infty$-category

Theory Appl. Categ. 32, 31-52 (2017)


We introduce a functor called the simplicial nerve of an $\Cal A_\infty$-category defined on the category of $\Cal A_\infty$-categories with values in simplicial sets. We show that the nerve of an $\Cal A_\infty$-category is an $(\infty,1)$-category in the sense of J. Lurie. This construction generalizes the nerve construction for differential graded categories given by Lurie. We prove that if a differential graded category is pretriangulated in the sense of A.I. Bondal and M. Kapranov then its nerve is a stable $(\infty,1)$-category in the sense of J. Lurie.

Mathematics Subject Classification



$\cal A_\infty$-categories, pretriangulated dg-categories, stable $(\infty,1)$-categories, simplicial sets, nerve, higher category theory