Steve Awodey - Category Theory Foundations, Lecture 1, Oregon Programming Languages Summer School 2012, University of Oregon
Homework excercises are available here: http://www.andrew.cmu.edu/user/awodey/SummerSchool/HW/
Topics covered in this lecture:
Definition of a category
Examples of categories (Set, Pos, Mon, Cat, others...)
Isomorphisms
Constructions (functors, product categories, arrow categories, slice categories)
Duality (opposite category, co- vs contravariant functors)
Examples of duality (functors into exponentials, representable functors)
For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/