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User:Michiexile/MATH198

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Course overview

Page is work in progress for background material for the Fall 2009 lecture course on Category Theory with a view towards applications that I am planning to give at Stanford University.

Single unit course. 10 lectures.

  • Functors.
  • Natural transformations.
  • Category of categories.
  • The power of dualization.
  • Limits, colimits.
  • Products, coproducts.
  • Equalizers, coequalizers.
  • Exponentials.
  • Power objects.
  • Monads.
  • Monoids.
  • Triples.
  • Cartesian Closed Categories.
    • Categorical logic.
  • Topoi.
    • Internal language and logic.
  • Haskell-Curry isomorphism.
  • Recursive categories.
  • Recursion as fixed points of monad algebras.
  • Recursion using special morphisms.
    • Hylo-
    • Zygo-
    • et.c.
  • User:Michiexile/SU09 Lecture 1
    • Category: Definition and examples.
    • Concrete categories.
      • Set.
      • Various categories capturing linear algebra.
    • Small categories.
      • Partial orders.
      • Monoids.
      • Finite groups.
    • Special morphisms
      • Epimorphism.
      • Monomorphism.
      • Isomorphism.
      • Endomorphism.
      • Automorphism.
    • Special objects
      • Initial.
      • Terminal.
      • Null.