2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/154884For a differential graded k-quiver Q we define the free A-infinity-category FQ generated by Q. The main result is that for an arbitrary A-infinity-category A the restriction A-infinity-functor A_\infty(FQ,A) -> A_1(Q,A) is an equivalence, where objects of the last A-infinity-category are morphisms of differential graded k-quivers Q -> A.32 pages, LaTeX, uses Paul Taylor's diagrams.sty. Close to published version. Resubmitted for TeXnical reasonsCategory Theorytext