Lecture Wednesday Jan 27

This meeting will cover Chapter 2 (Sheaves) up through 2.2.6. (plus examples 2.2.9 and 2.2.10).   The definition of sheaf is absolutely essential for what follows later in this course.

Read over the examples in 2.1.

  1. What is the definition of a presheaf on a topological space X?
  2. Do you see how differentiable functions on R^n can be made into a presheaf?
  3. Exercise 2.2.A. Aren’t we all category lovers?
  4. Do the terms “section” and “restriction” here carry their usual meanings?
  5. Work through the construction of the stalk at p of a presheaf.
  6. On a discrete topological space, how are the stalks related to sections?
  7. On the topological space X={p,q} with just three open sets {},{p},{p,q}, what is the stalk at q of a skyscraper sheaf at p?
  8. Do you see how the stalk is the colimit of a filtered index category?
  9. What two additional axioms make a presheaf a sheaf?
  10. Exercise 2.2.D.
  11. What is the constant presheaf on a topological space (Example 2.2.10.).
  12. How does the constant sheaf differ from the constant presheaf?