Difference between revisions of "User:Michiexile/MATH198"

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==Course overview==
  
==Course overview==
   
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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.
   
   
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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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* [[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.
   
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* [[User:Michiexile/SU09 Lecture 3]]
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* [[User:Michiexile/MATH198/Lecture 3]]
 
** Functors.
  
** Functors.
⚫
** Natural transformations.
  
 
** Category of categories.
  
** Category of categories.
  ⚫
** Natural transformations.
   
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* [[User:Michiexile/SU09 Lecture 4]]
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* [[User:Michiexile/MATH198/Lecture 4]]
  ⚫
** Products, coproducts.
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** Adjunctions.
  
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** Free and forgetful.
  
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* [[User:Michiexile/SU09 Lecture 5]]
  
 
** The power of dualization.
  
** The power of dualization.
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** The algebra of datatypes
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  +
  ⚫
* [[User:Michiexile/MATH198/Lecture 5]]
 
** Limits, colimits.
  
** Limits, colimits.
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⚫
** Products, coproducts.
  
  ⚫
* [[User:Michiexile/MATH198/Lecture 6]]
 
** Equalizers, coequalizers.
  
** Equalizers, coequalizers.
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** Pushouts/pullbacks
  ⚫
** Adjunctions.
  ⚫
** Free and forgetful.
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* [[User:Michiexile/SU09 Lecture 6]]
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* [[User:Michiexile/MATH198/Lecture 7]]
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** Monoids.
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** Monoid objects.
 
** Monads.
  
** Monads.
 
** Triples.
  
** Triples.
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** The Kleisli category.
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** Kleisli category.
 
** Monad factorization.
  
** Monad factorization.
   
  ⚫
* [[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
   
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* [[User:Michiexile/SU09 Lecture 7]]
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* [[User:Michiexile/MATH198/Lecture 9]]
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** Catamorphisms
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** Recursion as a categorical construction.
 
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** Anamorphisms
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** Recursive categories.
  
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** Hylomorphisms
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** Recursion as fixed points of monad algebras.
  
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** Metamorphisms
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** Recursion using special morphisms.
  
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** Paramorphisms
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*** Hylo-
  
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** Apomorphisms
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*** Zygo-
  
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** Properties of adjunctions, examples of adjunctions
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*** et.c.
  
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⚫
* [[User:Michiexile/SU09 Lecture 8]]
  
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** Topos.
  
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** Exponentials.
  
⚫
** Power objects.
  
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** Cartesian Closed Categories.
  
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⚫
* [[User:Michiexile/SU09 Lecture 9]]
  
⚫
** Internal logic.
  
   
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* [[User:Michiexile/SU09 Lecture 10]]
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* [[User:Michiexile/MATH198/Lecture 10]]
  ⚫
** Power objects
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** Review.
  
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** Classifying objects
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** Topoi
  ⚫
** Internal logic

Latest revision as of 05:51, 24 July 2010

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
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