# User:Michiexile/MATH198

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==Course overview== |
==Course overview== |
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− | 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. |

+ | |||

+ | Single unit course. 10 lectures. Each lecture is Wednesday 4.15-5.05 in 380F. |
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− | Single unit course. 10 lectures. |
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− | * Functors. |
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− | * Natural transformations. |
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− | * Category of categories. |
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− | * The power of dualization. |
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− | * Limits, colimits. |
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− | * Products, coproducts. |
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− | * Equalizers, coequalizers. |
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* Exponentials. |
* Exponentials. |
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* Power objects. |
* Power objects. |
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− | * Monads. |
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− | * Monoids. |
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− | * Triples. |
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* Cartesian Closed Categories. |
* Cartesian Closed Categories. |
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** Categorical logic. |
** Categorical logic. |
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Line 38: | Line 27: | ||

*** Monoids. |
*** Monoids. |
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*** Finite groups. |
*** Finite groups. |
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+ | |||

+ | |||

+ | * [[User:Michiexile/SU09 Lecture 2]] |
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** Special morphisms |
** Special morphisms |
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*** Epimorphism. |
*** Epimorphism. |
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*** Terminal. |
*** Terminal. |
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*** Null. |
*** Null. |
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− | |||

− | * [[User:Michiexile/SU09 Lecture 2]] |
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* [[User:Michiexile/SU09 Lecture 3]] |
* [[User:Michiexile/SU09 Lecture 3]] |
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+ | ** Functors. |
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+ | ** Natural transformations. |
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+ | ** Category of categories. |
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* [[User:Michiexile/SU09 Lecture 4]] |
* [[User:Michiexile/SU09 Lecture 4]] |
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+ | ** Adjunctions. |
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+ | ** Free and forgetful. |
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* [[User:Michiexile/SU09 Lecture 5]] |
* [[User:Michiexile/SU09 Lecture 5]] |
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+ | ** The power of dualization. |
||

+ | ** Limits, colimits. |
||

+ | ** Products, coproducts. |
||

+ | ** Equalizers, coequalizers. |
||

* [[User:Michiexile/SU09 Lecture 6]] |
* [[User:Michiexile/SU09 Lecture 6]] |
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+ | ** Monoids. |
||

+ | ** Monads. |
||

+ | ** Triples. |
||

+ | ** The Kleisli category. |
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+ | ** Monad factorization. |
||

+ | |||

* [[User:Michiexile/SU09 Lecture 7]] |
* [[User:Michiexile/SU09 Lecture 7]] |
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+ | ** Recursion as a categorical construction. |
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* [[User:Michiexile/SU09 Lecture 8]] |
* [[User:Michiexile/SU09 Lecture 8]] |
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+ | ** Topos. |
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* [[User:Michiexile/SU09 Lecture 9]] |
* [[User:Michiexile/SU09 Lecture 9]] |
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+ | ** Internal logic. |
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* [[User:Michiexile/SU09 Lecture 10]] |
* [[User:Michiexile/SU09 Lecture 10]] |
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+ | ** 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.