# User:Michiexile/MATH198

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Single unit course. 10 lectures. | Single unit course. 10 lectures. | ||

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* Functors. | * Functors. | ||

* Natural transformations. | * Natural transformations. | ||

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

+ | ** Category: Definition and examples. | ||

+ | ** Concrete categories. | ||

+ | *** Set. | ||

+ | *** Various categories capturing linear algebra. | ||

+ | ** Small categories. | ||

+ | *** Partial orders. | ||

+ | *** Monoids. | ||

+ | *** Finite groups. | ||

+ | ** Special morphisms | ||

+ | *** Epimorphism. | ||

+ | *** Monomorphism. | ||

+ | *** Isomorphism. | ||

+ | *** Endomorphism. | ||

+ | *** Automorphism. | ||

+ | ** Special objects | ||

+ | *** Initial. | ||

+ | *** Terminal. | ||

+ | *** Null. | ||

+ | |||

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

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

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

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

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

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

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

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

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

## Revision as of 11:53, 27 August 2009

## 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.

Single unit course. 10 lectures.

- Functors.
- Natural transformations.
- Category of categories.
- The power of dualization.
- Limits, colimits.
- Products, coproducts.
- Equalizers, coequalizers.
- Exponentials.
- Power objects.
- Monads.
- Monoids.
- Triples.
- 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.

- Special morphisms
- Epimorphism.
- Monomorphism.
- Isomorphism.
- Endomorphism.
- Automorphism.

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