Category Theory: July 11

Introductions

• Overview of the class; will provide outlines (such as this one!) for those who miss a class and want to keep up.

• Participant introductions

Algebra (for an excellent textbook, see Dummit and Foote, Abstract Algebra)

• History: Noether and Artin (20s), van der Waerden Modern Algebra (1930-31) [see https://www.ams.org/notices/199703/maclane.pdf]
  Category Theory itself was developed by Eilenberg and Mac Lane in the 40s. The first fundamental paper was "General theory of natural equivalences" (1945)
  [https://www.ams.org/journals/tran/1945-058-00/S0002-9947-1945-0013131-6/S0002-9947-1945-0013131-6.pdf]

• Groups

• Rings

• Fields

• Vector Spaces

• homomorphisms

Definition of a Category

• Stated the definition, but didn't have time for examples. We will review the definition at the start of next class, using Set as an example, and then give many more examples before continuing.