Geodesic
Simplicial Nerve of an $A_\infty$-category
Theory and applications of categories, Tome 32 (2017), pp. 31-52

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We introduce a functor called the simplicial nerve of an $A_\infty$-category defined on the category of $A_\infty$-categories with values in simplicial sets. We show that the nerve of an $A_\infty$-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.

Publié le :
Classification : 18G30
Keywords: $A_\infty$-categories, nerve, higher categories, pretriangulated dg-categories 
@article{TAC_2017_32_a1,
     author = {Giovanni Faonte},
     title = {Simplicial {Nerve} of an $A_\infty$-category},
     journal = {Theory and applications of categories},
     pages = {31--52},
     publisher = {mathdoc},
     volume = {32},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a1/}
}
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Giovanni Faonte. Simplicial Nerve of an $A_\infty$-category. Theory and applications of categories, Tome 32 (2017), pp. 31-52. http://geodesic.mathdoc.fr/item/TAC_2017_32_a1/