2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167748By counting with triangles and the octohedral axiom, we find a direct way to prove the formula of Toën in \cite{Toen2005} for a triangulated category with (left) homological-finite condition.12 pages. Final version, to appear in DukeQuantum AlgebraCategory Theory18E30, 16W30text