Lecture Friday Jan 22

Reading, Section 1.5 “Adjoints”

Study questions.  This section is largely a series of examples of adjoints.  Work through various examples.

  1. What is the definition of adjoint covariant functions.
  2. What does natural mean in the definition of adjoint?
  3. Exercises 1.5.A, 1.5.B, 1.5.C, 1.5.D, 1.5.E, 1.5.G.
  4. Can you interpret the free abelian group on a set as an adjoint to the forgetful functor from the category of abelian groups to the category of sets (which sends each abelian group to its underlying set)?

Lecture Wed Jan 20

The lecture will cover (1.4) limits and colimits.

Study questions.

  1. What is a small category?
  2. What is a diagram?
  3. What is the universal property characterizing a limit?
  4. Do you see how a product is a limit?
  5. Exercise 1.4.A.
  6. What is the universal property characterizing a colimit?
  7. Do you see how a coproduct is a colimit?
  8. Do you see how a union of sets (not necessarily disjoint) is a colimit?
  9. Exercise 1.4.B.
  10. What is a filtered poset? a filtered category?
  11. Exercise 1.4.C.
  12. Exercise 1.4.D.