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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.
   
* Category: Definition and examples.
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Single unit course. 10 lectures. Each lecture is Wednesday 4.15-5.05 in 380F.
* Concrete categories.
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** Set.
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** Various categories capturing linear algebra.
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* [[User:Michiexile/MATH198/Lecture 1]]
* Small categories.
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** Category: Definition and examples.
** Partial orders.
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** Concrete categories.
** Finite groups.
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*** Set.
* Special morphisms
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*** Various categories capturing linear algebra.
** Epimorphism.
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** Small categories.
** Monomorphism.
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*** Partial orders.
** Isomorphism.
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*** Monoids.
** Endomorphism.
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*** Finite groups.
** Automorphism.
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** Haskell-Curry isomorphism.
* Special objects
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** Initial.
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** Terminal.
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* [[User:Michiexile/MATH198/Lecture 2]]
** Null.
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** Special morphisms
* Functors.
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*** Epimorphism.
* Natural transformations.
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*** Monomorphism.
* Category of categories.
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*** Isomorphism.
* The power of dualization.
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*** Endomorphism.
* Limits, colimits.
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*** Automorphism.
* Products, coproducts.
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** Special objects
* Equalizers, coequalizers.
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*** Initial.
* Exponentials.
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*** Terminal.
* Power objects.
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*** Null.
* Monads.
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* Monoids.
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* [[User:Michiexile/MATH198/Lecture 3]]
* Triples.
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** Functors.
* Cartesian Closed Categories.
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** Category of categories.
** Categorical logic.
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** Natural transformations.
* Topoi.
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** Internal language and logic.
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* [[User:Michiexile/MATH198/Lecture 4]]
* Haskell-Curry isomorphism.
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** Products, coproducts.
* Recursive categories.
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** The power of dualization.
* Recursion as fixed points of monad algebras.
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** The algebra of datatypes
* Recursion using special morphisms.
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** Hylo-
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** Zygo-
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* [[User:Michiexile/MATH198/Lecture 5]]
** et.c.
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** Limits, colimits.
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* [[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