# 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. |
+ | 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/MATH198/Lecture 3]] |
* [[User:Michiexile/MATH198/Lecture 3]] |
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** Functors. |
** Functors. |
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− | ** Natural transformations. |
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** Category of categories. |
** Category of categories. |
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+ | ** Natural transformations. |
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* [[User:Michiexile/MATH198/Lecture 4]] |
* [[User:Michiexile/MATH198/Lecture 4]] |
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− | ** Adjunctions. |
+ | ** Products, coproducts. |

− | ** Free and forgetful. |
+ | ** The power of dualization. |

+ | ** The algebra of datatypes |
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+ | |||

* [[User:Michiexile/MATH198/Lecture 5]] |
* [[User:Michiexile/MATH198/Lecture 5]] |
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− | ** The power of dualization. |
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** Limits, colimits. |
** Limits, colimits. |
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− | ** Products, coproducts. |
+ | |

+ | * [[User:Michiexile/MATH198/Lecture 6]] |
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** Equalizers, coequalizers. |
** 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 6]] |
+ | |

− | ** Monoids. |
+ | * [[User:Michiexile/MATH198/Lecture 7]] |

+ | ** Monoid objects. |
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** Monads. |
** Monads. |
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** Triples. |
** Triples. |
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− | ** The Kleisli category. |
+ | ** Kleisli category. |

** Monad factorization. |
** Monad factorization. |
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− | |||

− | |||

− | * [[User:Michiexile/MATH198/Lecture 7]] |
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− | ** Recursion as a categorical construction. |
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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/MATH198/Lecture 8]] |
* [[User:Michiexile/MATH198/Lecture 8]] |
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− | ** Topos. |
+ | ** Algebras over monads |

− | ** Exponentials. |
+ | ** Algebras over endofunctors |

− | ** Power objects. |
+ | ** Initial algebras and recursion |

− | ** Cartesian Closed Categories. |
+ | ** Lambek's lemma |

* [[User:Michiexile/MATH198/Lecture 9]] |
* [[User:Michiexile/MATH198/Lecture 9]] |
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− | ** Internal logic. |
+ | ** Catamorphisms |

+ | ** 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]] |
* [[User:Michiexile/MATH198/Lecture 10]] |
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− | ** Review. |
+ | ** Power objects |

+ | ** 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 2
- Special morphisms
- Epimorphism.
- Monomorphism.
- Isomorphism.
- Endomorphism.
- Automorphism.

- Special objects
- Initial.
- Terminal.
- Null.

- Special morphisms

- 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
- Limits, colimits.

- User:Michiexile/MATH198/Lecture 6
- Equalizers, coequalizers.
- Pushouts/pullbacks
- Adjunctions.
- Free and forgetful.

- User:Michiexile/MATH198/Lecture 7
- Monoid objects.
- Monads.
- Triples.
- Kleisli category.
- Monad factorization.

- User:Michiexile/MATH198/Lecture 8
- Algebras over monads
- Algebras over endofunctors
- Initial algebras and recursion
- Lambek's lemma

- User:Michiexile/MATH198/Lecture 9
- Catamorphisms
- Anamorphisms
- Hylomorphisms
- Metamorphisms
- Paramorphisms
- Apomorphisms
- Properties of adjunctions, examples of adjunctions

- User:Michiexile/MATH198/Lecture 10
- Power objects
- Classifying objects
- Topoi
- Internal logic