# User:Michiexile/MATH198

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==Course overview== | ==Course overview== | ||

− | Page is work in progress for background material for the Fall 2009 lecture course on Category Theory with a view towards applications that I am planning to give at Stanford University. | + | 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. |

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

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* Exponentials. | * Exponentials. | ||

* Power objects. | * Power objects. | ||

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

** Categorical logic. | ** Categorical logic. | ||

Line 38: | Line 29: | ||

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

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

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+ | * [[User:Michiexile/SU09 Lecture 2]] | ||

** Special morphisms | ** Special morphisms | ||

*** Epimorphism. | *** Epimorphism. | ||

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*** Terminal. | *** Terminal. | ||

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

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* [[User:Michiexile/SU09 Lecture 3]] | * [[User:Michiexile/SU09 Lecture 3]] | ||

+ | ** Functors. | ||

+ | ** Natural transformations. | ||

+ | ** Category of categories. | ||

* [[User:Michiexile/SU09 Lecture 4]] | * [[User:Michiexile/SU09 Lecture 4]] | ||

+ | ** Adjunctions. | ||

+ | ** Free and forgetful. | ||

* [[User:Michiexile/SU09 Lecture 5]] | * [[User:Michiexile/SU09 Lecture 5]] | ||

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

+ | ** Limits, colimits. | ||

+ | ** Products, coproducts. | ||

+ | ** Equalizers, coequalizers. | ||

* [[User:Michiexile/SU09 Lecture 6]] | * [[User:Michiexile/SU09 Lecture 6]] | ||

+ | ** Monoids. | ||

+ | ** Monads. | ||

+ | ** Triples. | ||

+ | ** The Kleisli category. | ||

+ | ** Monad factorization. | ||

+ | |||

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

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

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

+ | ** Topos. | ||

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

+ | ** Internal logic. | ||

* [[User:Michiexile/SU09 Lecture 10]] | * [[User:Michiexile/SU09 Lecture 10]] | ||

+ | ** Review. |

## Revision as of 12:43, 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.

- Exponentials.
- Power objects.
- Cartesian Closed Categories.
- Categorical logic.

- Topoi.
- Internal language and logic.

- Haskell-Curry isomorphism.
- Recursive categories.
- Recursion as fixed points of monad algebras.
- Recursion using special morphisms.
- Hylo-
- Zygo-
- et.c.

- User:Michiexile/SU09 Lecture 1
- Category: Definition and examples.
- Concrete categories.
- Set.
- Various categories capturing linear algebra.

- Small categories.
- Partial orders.
- Monoids.
- Finite groups.

- 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.

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

- User:Michiexile/SU09 Lecture 10
- Review.