Course overview
This course is an introduction to category theory. Category theory is a kind of algebra that studies the fundamental structures that occur everywhere in mathematics: objects, relationships between them, relationships between relationships, and so on. Knowledge of basic category theory is useful to all mathematicians and essential to many. For example, modern algebraic geometry and algebraic topology could not exist without category theory. The categorical way of thinking enables the distinction of common patterns in diverse areas of mathematics and guides searches for appropriate definitions and fruitful conjectures. The course will pay particular attention to categorical structures in the areas of mathematics that the students in the course have studied previously.