Koszul duality for operadic categories

The aim of this sequel to arXiv:1812.02935 is set up the cornerstones Koszul duality and Koszulity in context operads over a large class operadic categories. In particular, for these categories we will study concrete examples binary quadratic operads, describe their duals prove that they are Koszul. This includes whose algebras most important operad- PROP-like structures such as classical variants cyclic, modular or wheeled also diverse versions PROPs properads, dioperads, 1/2PROPs, still more exotic objects permutads pre-permutads.