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* [[User:Michiexile/MATH198/Lecture 4]]
 
* [[User:Michiexile/MATH198/Lecture 4]]
** The power of dualization.
 
** Limits, colimits.
 
 
** Products, coproducts.
 
** Products, coproducts.
** Equalizers, coequalizers.
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** The power of dualization.
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** The algebra of datatypes
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* [[User:Michiexile/MATH198/Lecture 5]]
 
* [[User:Michiexile/MATH198/Lecture 5]]
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** Limits, colimits.
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** Equalizers, coequalizers.
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** Simulation using test suites.
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* [[User:Michiexile/MATH198/Lecture 6]]
 
** Adjunctions.
 
** Adjunctions.
 
** Free and forgetful.
 
** Free and forgetful.
  
* [[User:Michiexile/MATH198/Lecture 6]]
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** Monoids.
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* [[User:Michiexile/MATH198/Lecture 7]]
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** Monoid objects.
 
** Monads.
 
** Monads.
 
** Triples.
 
** Triples.
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** Monad factorization.
 
** Monad factorization.
  
 
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* [[User:Michiexile/MATH198/Lecture 8]]
* [[User:Michiexile/MATH198/Lecture 7]]
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** Recursion as a categorical construction.  
 
** Recursion as a categorical construction.  
 
** Recursive categories.
 
** Recursive categories.
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*** et.c.
 
*** et.c.
  
* [[User:Michiexile/MATH198/Lecture 8]]
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* [[User:Michiexile/MATH198/Lecture 9]]
 
** Topos.
 
** Topos.
 
** Exponentials.
 
** Exponentials.
 
** Power objects.
 
** Power objects.
 
** Cartesian Closed Categories.
 
** Cartesian Closed Categories.
 
* [[User:Michiexile/MATH198/Lecture 9]]
 
 
** Internal logic.
 
** Internal logic.
  
 
* [[User:Michiexile/MATH198/Lecture 10]]
 
* [[User:Michiexile/MATH198/Lecture 10]]
 
** Review.
 
** Review.

Revision as of 01:17, 8 October 2009

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.




  • User:Michiexile/MATH198/Lecture 8
    • Recursion as a categorical construction.
    • Recursive categories.
    • Recursion as fixed points of monad algebras.
    • Recursion using special morphisms.
      • Hylo-
      • Zygo-
      • et.c.