A Falcon false alarm

Done for the week and time to head home. I walk with great purpose across the lot headed to my car. Halfway, a darting form glides diagonally across my field of view and out of sight around the corner of a building. Those wings looked suspiciously Falcony. Slightly long front to back, a little short horizontally, and a distinctive curve to the wings. This could be my chance, I've been lugging around a telephoto lens in the trunk of the car for days. I know Cooper's hawks live around here, and I've seen Kestrels too. I divert to head around the corner and investigate. I see a small bird sat on the top of a building. Small, so could be a Kestrel. I edge closer, and the "Falcon" turns into a dove. Well, I've made this mistake before. I wonder if there's any relation between Falcons and Doves? The wing shapes are reminiscent of the others. Though, I think Dove's might be Passerines and Falcons Non-Passerines, so that would be a stretch. I'll have to use this as a learning opportunity.