Difference between revisions of "User:Michiexile/MATH198"
Jump to navigation
Jump to search
Michiexile (talk | contribs) |
Michiexile (talk | contribs) |
||
Line 33: | Line 33: | ||
** Functors. |
** Functors. |
||
** Category of categories. |
** Category of categories. |
||
− | |||
⚫ | |||
** Natural transformations. |
** Natural transformations. |
||
⚫ | |||
⚫ | |||
− | * [[User:Michiexile/MATH198/Lecture |
+ | * [[User:Michiexile/MATH198/Lecture 4]] |
** The power of dualization. |
** The power of dualization. |
||
** Limits, colimits. |
** Limits, colimits. |
||
** Products, coproducts. |
** Products, coproducts. |
||
** Equalizers, coequalizers. |
** Equalizers, coequalizers. |
||
+ | |||
⚫ | |||
⚫ | |||
⚫ | |||
* [[User:Michiexile/MATH198/Lecture 6]] |
* [[User:Michiexile/MATH198/Lecture 6]] |
Revision as of 23:15, 6 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
- The power of dualization.
- Limits, colimits.
- Products, coproducts.
- Equalizers, coequalizers.
- User:Michiexile/MATH198/Lecture 5
- Adjunctions.
- Free and forgetful.
- 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.