User:Michiexile/MATH198
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(Difference between revisions)
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| - | * [[User:Michiexile/ | + | * [[User:Michiexile/MATH198/Lecture 1]] |
** Category: Definition and examples. | ** Category: Definition and examples. | ||
** Concrete categories. | ** Concrete categories. | ||
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*** Null. | *** Null. | ||
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** Functors. | ** Functors. | ||
** Natural transformations. | ** Natural transformations. | ||
** Category of categories. | ** Category of categories. | ||
| - | * [[User:Michiexile/ | + | * [[User:Michiexile/MATH198/Lecture 4]] |
** Adjunctions. | ** Adjunctions. | ||
** Free and forgetful. | ** Free and forgetful. | ||
| - | * [[User:Michiexile/ | + | * [[User:Michiexile/MATH198/Lecture 5]] |
** The power of dualization. | ** The power of dualization. | ||
** Limits, colimits. | ** Limits, colimits. | ||
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** Equalizers, coequalizers. | ** Equalizers, coequalizers. | ||
| - | * [[User:Michiexile/ | + | * [[User:Michiexile/MATH198/Lecture 6]] |
** Monoids. | ** Monoids. | ||
** Monads. | ** Monads. | ||
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** Recursion as a categorical construction. | ** Recursion as a categorical construction. | ||
** Recursive categories. | ** Recursive categories. | ||
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*** et.c. | *** et.c. | ||
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** Topos. | ** Topos. | ||
** Exponentials. | ** Exponentials. | ||
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** Cartesian Closed Categories. | ** Cartesian Closed Categories. | ||
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** Internal logic. | ** Internal logic. | ||
| - | * [[User:Michiexile/ | + | * [[User:Michiexile/MATH198/Lecture 10]] |
** Review. | ** Review. | ||
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.
