A yoga system that predated the Buddhist school is Jain yoga. But since Jain sources postdate Buddhist ones, it is difficult to distinguish between the nature of the early Jain school and elements derived from other schools. Most of the other contemporary yoga systems alluded in the Upanishads and some Buddhist texts are lost to time.[note 12]
Equipment required? No. You don't need any equipment because you'll rely on your own body weight for resistance. But you'll probably want to use a yoga mat to keep you from sliding around in standing poses, and to cushion you while in seated and lying positions. Other, optional equipment includes a yoga ball for balance, a yoga block or two, and straps to help you reach for your feet or link your hands behind your back.
Core: Yes. There are yoga poses to target just about every core muscle. Want to tighten those love handles? Then prop yourself up on one arm and do a side plank. To really burn out the middle of your abs, you can do boat pose, in which you balance on your "sit bones" (the bony prominences at the base of your pelvic bones) and hold your legs up in the air.