# 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. | + | Single unit course. 10 lectures. Each lecture is Wednesday 4.15-5.05 in 380F. |

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

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

− | ** Set. | + | ** Category: Definition and examples. |

− | ** Various categories capturing linear algebra. | + | ** Concrete categories. |

− | * Small categories. | + | *** Set. |

− | ** Partial orders. | + | *** Various categories capturing linear algebra. |

− | ** Monoids. | + | ** Small categories. |

− | ** Finite groups. | + | *** Partial orders. |

− | * Special morphisms | + | *** Monoids. |

− | ** Epimorphism. | + | *** Finite groups. |

− | ** Monomorphism. | + | ** Haskell-Curry isomorphism. |

− | ** Isomorphism. | + | |

− | ** Endomorphism. | + | |

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

− | * Special objects | + | ** Special morphisms |

− | ** Initial. | + | *** Epimorphism. |

− | ** Terminal. | + | *** Monomorphism. |

− | ** Null. | + | *** Isomorphism. |

− | * Functors. | + | *** Endomorphism. |

− | * Natural transformations. | + | *** Automorphism. |

− | * | + | ** Special objects |

− | * The power of dualization. | + | *** Initial. |

− | * Limits, colimits. | + | *** Terminal. |

− | * | + | *** Null. |

− | * Equalizers, coequalizers. | + | |

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

− | * | + | ** Functors. |

− | * | + | ** Category of categories. |

− | * | + | ** Natural transformations. |

− | * Triples. | + | |

− | * | + | * [[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 |

## 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