# User:Michiexile/MATH198

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

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* [[User:Michiexile/SU09 Lecture 1]] | * [[User:Michiexile/SU09 Lecture 1]] | ||

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

*** Finite groups. | *** Finite groups. | ||

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

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* [[User:Michiexile/SU09 Lecture 7]] | * [[User:Michiexile/SU09 Lecture 7]] | ||

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

+ | ** Recursive categories. | ||

+ | ** Recursion as fixed points of monad algebras. | ||

+ | ** Recursion using special morphisms. | ||

+ | *** Hylo- | ||

+ | *** Zygo- | ||

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

* [[User:Michiexile/SU09 Lecture 8]] | * [[User:Michiexile/SU09 Lecture 8]] | ||

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

+ | ** Exponentials. | ||

+ | ** Power objects. | ||

+ | ** Cartesian Closed Categories. | ||

* [[User:Michiexile/SU09 Lecture 9]] | * [[User:Michiexile/SU09 Lecture 9]] |

## Revision as of 12:44, 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/SU09 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/SU09 Lecture 2
- Special morphisms
- Epimorphism.
- Monomorphism.
- Isomorphism.
- Endomorphism.
- Automorphism.

- Special objects
- Initial.
- Terminal.
- Null.

- Special morphisms

- User:Michiexile/SU09 Lecture 3
- Functors.
- Natural transformations.
- Category of categories.

- User:Michiexile/SU09 Lecture 4
- Adjunctions.
- Free and forgetful.

- User:Michiexile/SU09 Lecture 5
- The power of dualization.
- Limits, colimits.
- Products, coproducts.
- Equalizers, coequalizers.

- User:Michiexile/SU09 Lecture 6
- Monoids.
- Monads.
- Triples.
- The Kleisli category.
- Monad factorization.

- User:Michiexile/SU09 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/SU09 Lecture 8
- Topos.
- Exponentials.
- Power objects.
- Cartesian Closed Categories.

- User:Michiexile/SU09 Lecture 9
- Internal logic.

- User:Michiexile/SU09 Lecture 10
- Review.