Category theory, with its increasing role in computer science, has proved useful in the investigation of programming languages and other theoretical aspects of software engineering. As a bridge-building exercise, we introduce the category theory course into the computer science curriculum, the purpose of which includes building a unified framework to generalize the discrete structures of mathematical courses and providing an environment for formulating concepts of other software engineering courses. We develop a teaching schema, summarize our experiences, and give some suggestions for pedagogical techniques for the course.