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. | ||
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*** 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. | ||
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* [[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.
