2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153563In this paper we advance the program of using exceptional collections to understand the gauge theory description of a D-brane probing a Calabi-Yau singularity. To this end, we strengthen the connection between strong exceptional collections and fractional branes. To demonstrate our ideas, we derive a strong exceptional collection for every Y^{p,q} singularity, and also prove that this collection is simple.28 pages; v2 clarifications made to section 2High Energy Physics - Theorytext