Difference between revisions of "User:Michiexile/MATH198"
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* [[User:Michiexile/MATH198/Lecture 7]] |
* [[User:Michiexile/MATH198/Lecture 7]] |
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** Monoid objects. |
** Monoid objects. |
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** Monads. |
** Monads. |
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** Kleisli category. |
** Kleisli category. |
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** Monad factorization. |
** Monad factorization. |
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* [[User:Michiexile/MATH198/Lecture 9]] |
* [[User:Michiexile/MATH198/Lecture 9]] |
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+ | ** Yoneda Lemma. |
| + | *** Adjoints are unique up to isomorphism. |
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| − | ** Exponentials. |
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| − | ** Cartesian Closed Categories. |
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* [[User:Michiexile/MATH198/Lecture 10]] |
* [[User:Michiexile/MATH198/Lecture 10]] |
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** Review. |
** Review. |
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| + | ** Topos. |
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** Recursion as a categorical construction. |
** Recursion as a categorical construction. |
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Revision as of 22:23, 29 October 2009
Course overview
Page is work in progress for background material for the Fall 2009 lecture course MATH198[1] on Category Theory and Functional Programming 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.
- Category of categories.
- Natural transformations.
- User:Michiexile/MATH198/Lecture 4
- Products, coproducts.
- The power of dualization.
- The algebra of datatypes
- User:Michiexile/MATH198/Lecture 5
- Limits, colimits.
- User:Michiexile/MATH198/Lecture 6
- Equalizers, coequalizers.
- Pushouts/pullbacks
- Adjunctions.
- Free and forgetful.
- User:Michiexile/MATH198/Lecture 7
- Properties of adjunctions.
- Examples of adjunctions.
- Things that are not adjunctions.
- User:Michiexile/MATH198/Lecture 8
- Monoid objects.
- Monads.
- Triples.
- Kleisli category.
- Monad factorization.
- User:Michiexile/MATH198/Lecture 9
- Yoneda Lemma.
- Adjoints are unique up to isomorphism.
- Yoneda Lemma.
- Topos.
- Power objects.
- Internal logic.
- Recursion as a categorical construction.
- Recursive categories.
- Recursion as fixed points of monad algebras.
- Recursion using special morphisms.
- Hylo-
- Zygo-
- et.c.