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Course overview

Page is work in progress for background material for the Fall 2009 lecture course MATH198[1] on Category Theory and Functional Programming that I am planning to give at Stanford University.

Single unit course. 10 lectures. Each lecture is Wednesday 4.15-5.05 in 380F.

  • User:Michiexile/MATH198/Lecture 1
    • Category: Definition and examples.
    • Concrete categories.
      • Set.
      • Various categories capturing linear algebra.
    • Small categories.
      • Partial orders.
      • Monoids.
      • Finite groups.
    • Haskell-Curry isomorphism.

Things yet to cover:



Yoneda's lemma.

Freyd's functor theorem.

Adjunction properties and theorems.

Examples of Adjunctions.

    • Review.
    • Topos.
    • Power objects.
    • Internal logic.
    • Recursion as a categorical construction.
    • Recursive categories.
    • Recursion as fixed points of monad algebras.
    • Recursion using special morphisms.
      • Hylo-
      • Zygo-
      • et.c.
    • Properties of adjunctions.
    • Examples of adjunctions.
    • Things that are not adjunctions.
    • Yoneda Lemma.
      • Adjoints are unique up to isomorphism.