English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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 $A_{\infty}$-morphisms, extending a result proved by D.Fern\'andez and E. Herscovich. This leads to a functor between the category of$d$-pre-Calabi-Yau structures and the partial category of$A_{\infty}$-categories of the form $\mathcal{A}\oplus\mathcal{A}^*[d-1]$ with$\mathcal{A}$ a graded quiver and whose morphisms are the data of an$A_{\infty}$-structure on $\mathcal{A}\oplus\mathcal{B}^*[d-1]$ together with$A_{\infty}$-morphisms $\mathcal{A}[1]\oplus\mathcal{B}^*[d]\rightarrow\mathcal{A}[1]\oplus\mathcal{A}^*[d]$ and$\mathcal{A}[1]\oplus\mathcal{B}^*[d]\rightarrow\mathcal{B}[1]\oplus\mathcal{B}^*[d]$.

Morphisms of pre-Calabi-Yau categories and morphisms of cyclic $A_{\infty}$-categories