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* [[User:Michiexile/SU09 Lecture 1]]
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* [[User:Michiexile/SU09 Lecture 2]]
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* [[User:Michiexile/SU09 Lecture 10]]

Revision as of 10:38, 27 August 2009

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.

  • 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.
  • 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.