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.
^ James Mallinson, "Sāktism and Hathayoga," 28 June 2012.
^ Mangano, Kelsey M.; Sahni, Shivani; Kiel, Douglas P.; Tucker, Katherine L.; Dufour, Alyssa B.; Hannan, Marian T. (February 8, 2017). "Dietary protein is associated with musculoskeletal health independently of dietary pattern: the Framingham Third Generation Study". The American Journal of Clinical Nutrition. 105 (3): 714–722. doi:10.3945/ajcn.116.136762. PMC 5320406. PMID 28179224 – via ajcn.nutrition.org.
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.