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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 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.
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Single unit course. 10 lectures. Each lecture is Wednesday 4.15-5.05 in 380F.
   
* 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.
 
   
* [[User:Michiexile/SU09 Lecture 1]]
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* [[User:Michiexile/MATH198/Lecture 1]]
* [[User:Michiexile/SU09 Lecture 2]]
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** Category: Definition and examples.
* [[User:Michiexile/SU09 Lecture 3]]
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** Concrete categories.
* [[User:Michiexile/SU09 Lecture 4]]
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*** Set.
* [[User:Michiexile/SU09 Lecture 5]]
+
*** Various categories capturing linear algebra.
* [[User:Michiexile/SU09 Lecture 6]]
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** Small categories.
* [[User:Michiexile/SU09 Lecture 7]]
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*** Partial orders.
* [[User:Michiexile/SU09 Lecture 8]]
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*** Monoids.
* [[User:Michiexile/SU09 Lecture 9]]
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*** Finite groups.
* [[User:Michiexile/SU09 Lecture 10]]
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** Haskell-Curry isomorphism.
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  +
  +
* [[User:Michiexile/MATH198/Lecture 2]]
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** Special morphisms
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*** Epimorphism.
  +
*** Monomorphism.
  +
*** Isomorphism.
  +
*** Endomorphism.
  +
*** Automorphism.
  +
** Special objects
  +
*** Initial.
  +
*** Terminal.
  +
*** Null.
  +
  +
* [[User:Michiexile/MATH198/Lecture 3]]
  +
** Functors.
  +
** Category of categories.
  +
** Natural transformations.
  +
  +
* [[User:Michiexile/MATH198/Lecture 4]]
  +
** Products, coproducts.
  +
** The power of dualization.
  +
** The algebra of datatypes
  +
  +
  +
* [[User:Michiexile/MATH198/Lecture 5]]
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** Limits, colimits.
  +
  +
* [[User:Michiexile/MATH198/Lecture 6]]
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** Equalizers, coequalizers.
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** Pushouts/pullbacks
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** Adjunctions.
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** Free and forgetful.
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* [[User:Michiexile/MATH198/Lecture 7]]
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** Monoid objects.
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** Monads.
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** Triples.
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** Kleisli category.
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** 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
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* [[User:Michiexile/MATH198/Lecture 9]]
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** Catamorphisms
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** Anamorphisms
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** Hylomorphisms
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** Metamorphisms
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** Paramorphisms
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** Apomorphisms
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** Properties of adjunctions, examples of adjunctions
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* [[User:Michiexile/MATH198/Lecture 10]]
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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