Computer Laboratory

Course pages 2016–17

Category Theory and Logic

Lecture slides and notes

Lecture summaries

  • Lecture 1: Introduction; some history; content of this course. Definition of category. The category of sets and functions. Commutative diagrams. Alternative definitions of category.
  • Lecture 2: Examples of categories: pre-ordered sets and monotone functions; monoids and monoid homomorphisms; a pre-ordered set as a category; a monoid as a category. Definition of isomorphism.
  • Lecture 3: Terminal objects. The opposite of a category and the duality principle. Initial objects. Free monoids as initial objects.
  • Lecture 4: Binary products and coproducts.
  • Lecture 5: Exponential objects: in the category of sets and in general. Cartesian closed categories: definition and examples.
  • Lecture 6: Intuitionistic Propositional Logic (IPL) in Natural Deduction style. Semantics of IPL in a cartesian closed pre-ordered set.

Exercise sheets

Office hours

  • The module lecturer will be available to answer questions about the course material and exercises on Wednesdays between 12:00 and 13:00 in FC08 during Full Term.

Additional material