Week 1: Course overview. Definition and examples of categories. Classes and sets. Small and locally small categories. Isomorphisms. Subcategories. Duality. Monos and epis. Slice categories.
Week 2: Functors
Week 3: Sketch of Singular homology
Week 4: Natural transformations
Week 5: Representable functors
Week 6: Yoneda's Lemma