# User:Michiexile/MATH198

### From HaskellWiki

< User:Michiexile(Difference between revisions)

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

Line 52: | Line 52: | ||

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

+ | ** Properties of adjunctions. |
||

+ | ** Examples of adjunctions. |
||

+ | ** Things that are not adjunctions. |
||

+ | |||

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

** Monoid objects. |
** Monoid objects. |
||

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

Line 57: | Line 62: | ||

** Kleisli category. |
** Kleisli category. |
||

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

− | |||

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

− | ** Properties of adjunctions. |
||

− | ** Examples of adjunctions. |
||

− | ** Things that are not adjunctions. |
||

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

− | ** Topos. |
+ | ** Yoneda Lemma. |

− | ** Exponentials. |
+ | *** Adjoints are unique up to isomorphism. |

− | ** Power objects. |
||

− | ** Cartesian Closed Categories. |
||

− | ** Internal logic. |
||

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

** Review. |
** Review. |
||

+ | |||

+ | ** Topos. |
||

+ | ** Power objects. |
||

+ | ** Internal logic. |
||

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

## Revision as of 22:23, 29 October 2009

## Course overview

Page is work in progress for background material for the Fall 2009 lecture course MATH198[1] on Category Theory and Functional Programming 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.
- 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
- Properties of adjunctions.
- Examples of adjunctions.
- Things that are not adjunctions.

- User:Michiexile/MATH198/Lecture 8
- Monoid objects.
- Monads.
- Triples.
- Kleisli category.
- Monad factorization.

- User:Michiexile/MATH198/Lecture 9
- Yoneda Lemma.
- Adjoints are unique up to isomorphism.

- Yoneda Lemma.

- Topos.
- Power objects.
- Internal logic.

- Recursion as a categorical construction.
- Recursive categories.
- Recursion as fixed points of monad algebras.
- Recursion using special morphisms.
- Hylo-
- Zygo-
- et.c.