User:Michiexile/MATH198

Course overview

Page is the background material for the Fall 2009 lecture course MATH198[1] on Category Theory and Functional Programming that I gave 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.

• User:Michiexile/MATH198/Lecture 2
  • Special morphisms
    • Epimorphism.
    • Monomorphism.
    • Isomorphism.
    • Endomorphism.
    • Automorphism.
  • Special objects
    • Initial.
    • Terminal.
    • Null.

• User:Michiexile/MATH198/Lecture 3
  • Functors.
  • Category of categories.
  • Natural transformations.

• User:Michiexile/MATH198/Lecture 4
  • Products, coproducts.
  • The power of dualization.
  • The algebra of datatypes

• User:Michiexile/MATH198/Lecture 5
  • Limits, colimits.

• User:Michiexile/MATH198/Lecture 6
  • Equalizers, coequalizers.
  • Pushouts/pullbacks
  • Adjunctions.
  • Free and forgetful.

• User:Michiexile/MATH198/Lecture 7
  • Monoid objects.
  • Monads.
  • Triples.
  • Kleisli category.
  • Monad factorization.

• User:Michiexile/MATH198/Lecture 8
  • Algebras over monads
  • Algebras over endofunctors
  • Initial algebras and recursion
  • Lambek's lemma

• User:Michiexile/MATH198/Lecture 9
  • Catamorphisms
  • Anamorphisms
  • Hylomorphisms
  • Metamorphisms
  • Paramorphisms
  • Apomorphisms
  • Properties of adjunctions, examples of adjunctions

• User:Michiexile/MATH198/Lecture 10
  • Power objects
  • Classifying objects
  • Topoi
  • Internal logic