This study proposes a new way of understanding cell transformations by using category theory to build a formal structure called the Category of Cells (CELL). Rather than treating cellular processes in isolation, the framework organizes cells and their transformations within a unified mathematical setting. The study examines fundamental categorical properties of CELL such as the existence of initial and terminal objects and its connectedness to better understand structural relationships between different cell types. To elucidate cellular hierarchies and potential transformation processes, biologically relevant subcategories are investigated, such as terminally differentiated cells and differentiated somatic cells. The structure represents intricate biological processes including cell differentiation, cellular reprogramming, and oncogenesis using categorical tools like slice categories and arrow categories.