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User:Michiexile/MATH198

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==Course overview==
 
==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.
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Page is the background material for the Fall 2009 lecture course MATH198[http://coursework.stanford.edu/homepage/F09/F09-MATH-198-01.html] 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.
 
Single unit course. 10 lectures. Each lecture is Wednesday 4.15-5.05 in 380F.
  
  
* Exponentials.
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* [[User:Michiexile/MATH198/Lecture 1]]
* Power objects.
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* Cartesian Closed Categories.
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** Categorical logic.
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* Topoi.
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** Internal language and logic.
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* Haskell-Curry isomorphism.
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* Recursive categories.
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* Recursion as fixed points of monad algebras.
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* Recursion using special morphisms.
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** Hylo-
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** Zygo-
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** et.c.
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* [[User:Michiexile/SU09 Lecture 1]]
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** Category: Definition and examples.
 
** Category: Definition and examples.
 
** Concrete categories.
 
** Concrete categories.
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*** Monoids.
 
*** Monoids.
 
*** Finite groups.
 
*** Finite groups.
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** Haskell-Curry isomorphism.
  
  
* [[User:Michiexile/SU09 Lecture 2]]
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* [[User:Michiexile/MATH198/Lecture 2]]
 
** Special morphisms
 
** Special morphisms
 
*** Epimorphism.
 
*** Epimorphism.
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*** Null.
 
*** Null.
  
* [[User:Michiexile/SU09 Lecture 3]]
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* [[User:Michiexile/MATH198/Lecture 3]]
 
** Functors.
 
** Functors.
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** Category of categories.
 
** Natural transformations.
 
** Natural transformations.
** Category of categories.
 
  
* [[User:Michiexile/SU09 Lecture 4]]
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* [[User:Michiexile/MATH198/Lecture 4]]
** Adjunctions.
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** Products, coproducts.
** Free and forgetful.
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** The power of dualization.
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** The algebra of datatypes
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* [[User:Michiexile/SU09 Lecture 5]]
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* [[User:Michiexile/MATH198/Lecture 5]]
** The power of dualization.
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** Limits, colimits.
 
** Limits, colimits.
** Products, coproducts.
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* [[User:Michiexile/MATH198/Lecture 6]]
 
** Equalizers, coequalizers.
 
** Equalizers, coequalizers.
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** Pushouts/pullbacks
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** Adjunctions.
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** Free and forgetful.
  
* [[User:Michiexile/SU09 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.
** The Kleisli category.
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** Kleisli category.
 
** Monad factorization.
 
** Monad factorization.
  
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* [[User:Michiexile/MATH198/Lecture 8]]
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** Algebras over monads
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** Algebras over endofunctors
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** Initial algebras and recursion
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** Lambek's lemma
  
* [[User:Michiexile/SU09 Lecture 7]]
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* [[User:Michiexile/MATH198/Lecture 9]]
** Recursion as a categorical construction.
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** Catamorphisms
 
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** Anamorphisms
* [[User:Michiexile/SU09 Lecture 8]]
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** Hylomorphisms
** Topos.
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** Metamorphisms
 
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** Paramorphisms
* [[User:Michiexile/SU09 Lecture 9]]
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** Apomorphisms
** Internal logic.
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** Properties of adjunctions, examples of adjunctions
  
* [[User:Michiexile/SU09 Lecture 10]]
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* [[User:Michiexile/MATH198/Lecture 10]]
** Review.
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** Power objects
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** Classifying objects
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** Topoi
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** Internal logic

Latest revision as of 05:51, 24 July 2010

[edit] 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 9
    • Catamorphisms
    • Anamorphisms
    • Hylomorphisms
    • Metamorphisms
    • Paramorphisms
    • Apomorphisms
    • Properties of adjunctions, examples of adjunctions