User:Michiexile/MATH198
From HaskellWiki
(Difference between revisions)
| Line 36: | Line 36: | ||
* [[User:Michiexile/MATH198/Lecture 4]] | * [[User:Michiexile/MATH198/Lecture 4]] | ||
| - | |||
| - | |||
** Products, coproducts. | ** Products, coproducts. | ||
| - | ** | + | ** The power of dualization. |
| + | ** The algebra of datatypes | ||
| + | |||
* [[User:Michiexile/MATH198/Lecture 5]] | * [[User:Michiexile/MATH198/Lecture 5]] | ||
| + | ** Limits, colimits. | ||
| + | ** Equalizers, coequalizers. | ||
| + | ** Simulation using test suites. | ||
| + | |||
| + | * [[User:Michiexile/MATH198/Lecture 6]] | ||
** Adjunctions. | ** Adjunctions. | ||
** Free and forgetful. | ** Free and forgetful. | ||
| - | * [[User:Michiexile/MATH198/Lecture | + | |
| - | ** | + | * [[User:Michiexile/MATH198/Lecture 7]] |
| + | ** Monoid objects. | ||
** Monads. | ** Monads. | ||
** Triples. | ** Triples. | ||
| Line 52: | Line 58: | ||
** Monad factorization. | ** Monad factorization. | ||
| - | + | * [[User:Michiexile/MATH198/Lecture 8]] | |
| - | * [[User:Michiexile/MATH198/Lecture | + | |
** Recursion as a categorical construction. | ** Recursion as a categorical construction. | ||
** Recursive categories. | ** Recursive categories. | ||
| Line 62: | Line 67: | ||
*** et.c. | *** et.c. | ||
| - | * [[User:Michiexile/MATH198/Lecture | + | * [[User:Michiexile/MATH198/Lecture 9]] |
** Topos. | ** Topos. | ||
** Exponentials. | ** Exponentials. | ||
** Power objects. | ** Power objects. | ||
** Cartesian Closed Categories. | ** Cartesian Closed Categories. | ||
| - | |||
| - | |||
** Internal logic. | ** Internal logic. | ||
* [[User:Michiexile/MATH198/Lecture 10]] | * [[User:Michiexile/MATH198/Lecture 10]] | ||
** Review. | ** Review. | ||
Revision as of 01:17, 8 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.
- Equalizers, coequalizers.
- Simulation using test suites.
- User:Michiexile/MATH198/Lecture 6
- Adjunctions.
- Free and forgetful.
- User:Michiexile/MATH198/Lecture 7
- Monoid objects.
- Monads.
- Triples.
- The Kleisli category.
- Monad factorization.
- User:Michiexile/MATH198/Lecture 8
- 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 9
- Topos.
- Exponentials.
- Power objects.
- Cartesian Closed Categories.
- Internal logic.
