Theory of Categories; Object or Tool
How important is the theory of categories? From the early days of its creation until today, this question has occupied the minds of mathematicians and different answers have been provided: For some categories are merely a tool. For others, they are a fundamental part of today’s mathematics. Generally, questions like these do not have definite and absolute answers. At least for this particular question, the mathematics community has not reached a common answer, and probably will never reach a resolution. Our goal in writing this article is to discuss the origins and developments of the theory of categories and also discuss its role in mathematics.