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* [[User:Michiexile/SU09 Lecture 1]]
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* [[User:Michiexile/MATH198/Lecture 1]]
 
** Category: Definition and examples.
 
** Category: Definition and examples.
 
** Concrete categories.
 
** Concrete categories.
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*** Null.
 
*** Null.
   
* [[User:Michiexile/SU09 Lecture 3]]
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* [[User:Michiexile/MATH198/Lecture 3]]
 
** Functors.
 
** Functors.
 
** Natural transformations.
 
** Natural transformations.
 
** Category of categories.
 
** Category of categories.
   
* [[User:Michiexile/SU09 Lecture 4]]
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* [[User:Michiexile/MATH198/Lecture 4]]
 
** Adjunctions.
 
** Adjunctions.
 
** Free and forgetful.
 
** Free and forgetful.
   
* [[User:Michiexile/SU09 Lecture 5]]
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* [[User:Michiexile/MATH198/Lecture 5]]
 
** The power of dualization.
 
** The power of dualization.
 
** Limits, colimits.
 
** Limits, colimits.
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** Equalizers, coequalizers.
 
** Equalizers, coequalizers.
   
* [[User:Michiexile/SU09 Lecture 6]]
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* [[User:Michiexile/MATH198/Lecture 6]]
 
** Monoids.
 
** Monoids.
 
** Monads.
 
** Monads.
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* [[User:Michiexile/SU09 Lecture 7]]
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* [[User:Michiexile/MATH198/Lecture 7]]
 
** Recursion as a categorical construction.
 
** Recursion as a categorical construction.
 
** Recursive categories.
 
** Recursive categories.
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*** et.c.
 
*** et.c.
   
* [[User:Michiexile/SU09 Lecture 8]]
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* [[User:Michiexile/MATH198/Lecture 8]]
 
** Topos.
 
** Topos.
 
** Exponentials.
 
** Exponentials.
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** Cartesian Closed Categories.
 
** Cartesian Closed Categories.
   
* [[User:Michiexile/SU09 Lecture 9]]
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* [[User:Michiexile/MATH198/Lecture 9]]
 
** Internal logic.
 
** Internal logic.
   
* [[User:Michiexile/SU09 Lecture 10]]
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* [[User:Michiexile/MATH198/Lecture 10]]
 
** Review.
 
** Review.

Revision as of 12:48, 3 September 2009

Course overview

Page is work in progress for background material for the Fall 2009 lecture course MATH198 on Category Theory with a view towards applications 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.



  • User:Michiexile/MATH198/Lecture 7
    • Recursion as a categorical construction.
    • Recursive categories.
    • Recursion as fixed points of monad algebras.
    • Recursion using special morphisms.
      • Hylo-
      • Zygo-
      • et.c.