2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123623We give a complete description of the relationship between the vanishing cycles of a complex of sheaves along a function $f$ and Thom's $a_f$ condition.14 pages, with a revised introductionAlgebraic Geometry32B15, 32C35, 32C18, 32B10text