# User:Michiexile/MATH198

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==Course overview== | ==Course overview== | ||

− | Page is | + | 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. | ||

− | * [[User:Michiexile/ | + | * [[User:Michiexile/MATH198/Lecture 1]] |

** Category: Definition and examples. | ** Category: Definition and examples. | ||

** Concrete categories. | ** Concrete categories. | ||

Line 18: | Line 18: | ||

− | * [[User:Michiexile/ | + | * [[User:Michiexile/MATH198/Lecture 2]] |

** Special morphisms | ** Special morphisms | ||

*** Epimorphism. | *** Epimorphism. | ||

Line 30: | Line 30: | ||

*** Null. | *** Null. | ||

− | * [[User:Michiexile/ | + | * [[User:Michiexile/MATH198/Lecture 3]] |

** Functors. | ** Functors. | ||

− | |||

** Category of categories. | ** Category of categories. | ||

+ | ** Natural transformations. | ||

− | * [[User:Michiexile/ | + | * [[User:Michiexile/MATH198/Lecture 4]] |

− | ** | + | ** Products, coproducts. |

− | + | ||

− | + | ||

− | + | ||

** The power of dualization. | ** The power of dualization. | ||

+ | ** The algebra of datatypes | ||

+ | |||

+ | |||

+ | * [[User:Michiexile/MATH198/Lecture 5]] | ||

** Limits, colimits. | ** Limits, colimits. | ||

− | * | + | |

+ | * [[User:Michiexile/MATH198/Lecture 6]] | ||

** Equalizers, coequalizers. | ** Equalizers, coequalizers. | ||

+ | ** Pushouts/pullbacks | ||

+ | ** Adjunctions. | ||

+ | ** Free and forgetful. | ||

+ | |||

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

− | ** | + | ** Monoid objects. |

** Monads. | ** Monads. | ||

** Triples. | ** Triples. | ||

− | ** | + | ** Kleisli category. |

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

+ | * [[User:Michiexile/MATH198/Lecture 8]] | ||

+ | ** Algebras over monads | ||

+ | ** Algebras over endofunctors | ||

+ | ** Initial algebras and recursion | ||

+ | ** Lambek's lemma | ||

− | * [[User:Michiexile/ | + | * [[User:Michiexile/MATH198/Lecture 9]] |

− | ** | + | ** Catamorphisms |

− | ** | + | ** Anamorphisms |

− | ** | + | ** Hylomorphisms |

− | ** | + | ** Metamorphisms |

− | ** | + | ** Paramorphisms |

− | ** | + | ** Apomorphisms |

− | ** | + | ** Properties of adjunctions, examples of adjunctions |

− | + | ||

− | + | ||

− | + | ||

− | + | ||

− | + | ||

− | + | ||

− | + | ||

− | + | ||

− | + | ||

− | * [[User:Michiexile/ | + | * [[User:Michiexile/MATH198/Lecture 10]] |

− | ** | + | ** Power objects |

+ | ** Classifying objects | ||

+ | ** Topoi | ||

+ | ** 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