2023/04/26 by Marion Boucrot, Boucrot, Marion · 1 voice
Mathematics · #Category Theory (math.CT) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.CT #math.KT
paper · pdf · doi:10.48550/arxiv.2304.13661
arxiv published 2023/04/26 · arxiv updated 2024/04/05
In this article we prove that there exists a relation between d-pre-Calabi-Yau morphisms introduced by M. Kontsevich, A. Takeda and Y. Vlassopoulos and cyclic A∞-morphisms, extending a result proved by D. Fernández and E. Herscovich. This leads to a functor between the category of d-pre-Calabi-Yau structures and the partial category of A∞-categories of the form A\oplusA^*[d-1] with A a graded quiver and whose morphisms are the data of an A∞-structure on A\oplusB^*[d-1] together with A∞-morphisms A[1]\oplusB^*[d]→ A[1]\oplusA^*[d] and A[1]\oplusB^*[d]→ B[1]\oplusB^*[d].