# User:Michiexile/MATH198

### From HaskellWiki

< User:Michiexile(Difference between revisions)

Michiexile (Talk | contribs) |
Michiexile (Talk | contribs) |
||

Line 6: | Line 6: | ||

− | * [[User:Michiexile/SU09 Lecture 1]] |
+ | * [[User:Michiexile/MATH198/Lecture 1]] |

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

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

Line 30: | Line 30: | ||

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

− | * [[User:Michiexile/SU09 Lecture 3]] |
+ | * [[User:Michiexile/MATH198/Lecture 3]] |

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

** Natural transformations. |
** Natural transformations. |
||

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

− | * [[User:Michiexile/SU09 Lecture 4]] |
+ | * [[User:Michiexile/MATH198/Lecture 4]] |

** Adjunctions. |
** Adjunctions. |
||

** Free and forgetful. |
** Free and forgetful. |
||

− | * [[User:Michiexile/SU09 Lecture 5]] |
+ | * [[User:Michiexile/MATH198/Lecture 5]] |

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

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

Line 45: | Line 45: | ||

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

− | * [[User:Michiexile/SU09 Lecture 6]] |
+ | * [[User:Michiexile/MATH198/Lecture 6]] |

** Monoids. |
** Monoids. |
||

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

Line 53: | Line 53: | ||

− | * [[User:Michiexile/SU09 Lecture 7]] |
+ | * [[User:Michiexile/MATH198/Lecture 7]] |

** Recursion as a categorical construction. |
** Recursion as a categorical construction. |
||

** Recursive categories. |
** Recursive categories. |
||

Line 62: | Line 62: | ||

*** et.c. |
*** et.c. |
||

− | * [[User:Michiexile/SU09 Lecture 8]] |
+ | * [[User:Michiexile/MATH198/Lecture 8]] |

** Topos. |
** Topos. |
||

** Exponentials. |
** Exponentials. |
||

Line 68: | Line 68: | ||

** Cartesian Closed Categories. |
** Cartesian Closed Categories. |
||

− | * [[User:Michiexile/SU09 Lecture 9]] |
+ | * [[User:Michiexile/MATH198/Lecture 9]] |

** Internal logic. |
** Internal logic. |
||

− | * [[User:Michiexile/SU09 Lecture 10]] |
+ | * [[User:Michiexile/MATH198/Lecture 10]] |

** Review. |
** Review. |

## Revision as of 12:48, 3 September 2009

## Course overview

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.

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.
- Natural transformations.
- Category of categories.

- User:Michiexile/MATH198/Lecture 4
- Adjunctions.
- Free and forgetful.

- User:Michiexile/MATH198/Lecture 5
- The power of dualization.
- Limits, colimits.
- Products, coproducts.
- Equalizers, coequalizers.

- User:Michiexile/MATH198/Lecture 6
- Monoids.
- Monads.
- Triples.
- The Kleisli category.
- Monad factorization.

- User:Michiexile/MATH198/Lecture 7
- Recursion as a categorical construction.
- Recursive categories.
- Recursion as fixed points of monad algebras.
- Recursion using special morphisms.
- Hylo-
- Zygo-
- et.c.

- User:Michiexile/MATH198/Lecture 8
- Topos.
- Exponentials.
- Power objects.
- Cartesian Closed Categories.

- User:Michiexile/MATH198/Lecture 9
- Internal logic.