This study tracks the progress of Suhrawardis philosophy focusing on his critique of the axial doctrine of the categories and topics related to it: predication and hylomorphism. While its known that he rejected hylomorphism and reduced the categories into five, its not known how and in which context he has achieved his positions. This is a philosophical study with an eye on the history of concepts. Each chapter detects the historical development from Aristotle through his commentators to Avicenna and critical Avicennans, and then to Suhrawardi. Suhrawardi discerns two diverging projects in the Categories: An ontological project of the ten highest genera of being, and a project of predication embodied in Aristotles predicative square. He discusses the latter in the Isagoge, whereas the former is discussed and reduced to five (substance, quality, quantity, relation, motion) in metaphysics. He also shifts hylomorphism from metaphysics - its Avicennan locus - to physics. Perhaps for this reason scholars never paid attention to his proper texts for the theory of body and confined themselves with the polemics of Hikmat al-israq. This is the first study of physics and general metaphysics of al-Talwihat, al-Masari, and al-Muqawamat.