Difference between revisions of "User:Michiexile/MATH198"
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+ | * [[User:Michiexile/MATH198/Lecture 1]] |
** Category: Definition and examples. |
** Category: Definition and examples. |
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** Concrete categories. |
** Concrete categories. |
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*** Null. |
*** Null. |
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+ | * [[User:Michiexile/MATH198/Lecture 3]] |
** Functors. |
** Functors. |
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** Natural transformations. |
** Natural transformations. |
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** Category of categories. |
** Category of categories. |
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+ | * [[User:Michiexile/MATH198/Lecture 4]] |
** Adjunctions. |
** Adjunctions. |
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** Free and forgetful. |
** Free and forgetful. |
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+ | * [[User:Michiexile/MATH198/Lecture 5]] |
** The power of dualization. |
** The power of dualization. |
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** Limits, colimits. |
** Limits, colimits. |
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** Equalizers, coequalizers. |
** Equalizers, coequalizers. |
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+ | * [[User:Michiexile/MATH198/Lecture 6]] |
** Monoids. |
** Monoids. |
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** Monads. |
** Monads. |
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+ | * [[User:Michiexile/MATH198/Lecture 7]] |
** Recursion as a categorical construction. |
** Recursion as a categorical construction. |
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** Recursive categories. |
** Recursive categories. |
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*** et.c. |
*** et.c. |
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** Topos. |
** Topos. |
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** Exponentials. |
** Exponentials. |
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** Cartesian Closed Categories. |
** Cartesian Closed Categories. |
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+ | * [[User:Michiexile/MATH198/Lecture 9]] |
** Internal logic. |
** Internal logic. |
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| − | * [[User:Michiexile/ |
+ | * [[User:Michiexile/MATH198/Lecture 10]] |
** Review. |
** Review. |
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Revision as of 12:48, 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/MATH198/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/MATH198/Lecture 2
- Special morphisms
- Epimorphism.
- Monomorphism.
- Isomorphism.
- Endomorphism.
- Automorphism.
- Special objects
- Initial.
- Terminal.
- Null.
- Special morphisms
- User:Michiexile/MATH198/Lecture 3
- Functors.
- Natural transformations.
- Category of categories.
- User:Michiexile/MATH198/Lecture 4
- Adjunctions.
- Free and forgetful.
- User:Michiexile/MATH198/Lecture 5
- The power of dualization.
- Limits, colimits.
- Products, coproducts.
- Equalizers, coequalizers.
- User:Michiexile/MATH198/Lecture 6
- Monoids.
- Monads.
- Triples.
- The Kleisli category.
- Monad factorization.
- User:Michiexile/MATH198/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/MATH198/Lecture 8
- Topos.
- Exponentials.
- Power objects.
- Cartesian Closed Categories.
- User:Michiexile/MATH198/Lecture 9
- Internal logic.