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 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.
   
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Single unit course. 10 lectures.
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Single unit course. 10 lectures. Each lecture is Wednesday 4.15-5.05 in 380F.
   
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⚫
* Category: Definition and examples.
  
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* [[User:Michiexile/MATH198/Lecture 1]]
⚫
* Concrete categories.
  
  ⚫
** Category: Definition and examples.
⚫
** Set.
  
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** Various categories capturing linear algebra.
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** Concrete categories.
  ⚫
*** Set.
⚫
* Small categories.
  
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*** Various categories capturing linear algebra.
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** Partial orders.
  
  ⚫
** Small categories.
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** Monoids.
  
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** Finite groups.
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*** Partial orders.
  ⚫
*** Monoids.
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* Special morphisms
  
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** Epimorphism.
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*** Finite groups.
  ⚫
** Haskell-Curry isomorphism.
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** Monomorphism.
  
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** Isomorphism.
  
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⚫
** Endomorphism.
  
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* [[User:Michiexile/MATH198/Lecture 2]]
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** Automorphism.
  
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* Special objects
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** Special morphisms
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** Initial.
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*** Epimorphism.
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** Terminal.
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*** Monomorphism.
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** Null.
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*** Isomorphism.
  ⚫
*** Endomorphism.
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* Functors.
  
  ⚫
*** Automorphism.
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* Natural transformations.
  
  ⚫
** Special objects
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* Category of categories.
  
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*** Initial.
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* The power of dualization.
  
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*** Terminal.
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* Limits, colimits.
  
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*** Null.
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* Products, coproducts.
  
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⚫
* Equalizers, coequalizers.
  
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* [[User:Michiexile/MATH198/Lecture 3]]
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* Exponentials.
  
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** Functors.
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* Power objects.
  
  ⚫
** Category of categories.
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* Monads.
  
  ⚫
** Natural transformations.
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* Monoids.
  
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⚫
* Triples.
  
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* [[User:Michiexile/MATH198/Lecture 4]]
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* Cartesian Closed Categories.
  
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** Products, coproducts.
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** Categorical logic.
  
  ⚫
** The power of dualization.
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* Topoi.
  
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** The algebra of datatypes
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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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* [[User:Michiexile/MATH198/Lecture 5]]
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* Recursion as fixed points of monad algebras.
  
  ⚫
** Limits, colimits.
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* Recursion using special morphisms.
  
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** Hylo-
  
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* [[User:Michiexile/MATH198/Lecture 6]]
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** Zygo-
  
  ⚫
** Equalizers, coequalizers.
⚫
** et.c.
  
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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.
  ⚫
** 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]]
  ⚫
** Power objects
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** Classifying objects
  ⚫
** 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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