Difference between revisions of "User:Michiexile/MATH198"
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* [[User:Michiexile/MATH198/Lecture 8]] |
* [[User:Michiexile/MATH198/Lecture 8]] |
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| + | ** Algebras over monads |
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| + | ** Algebras over endofunctors |
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| + | ** Initial algebras and recursion |
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| ⚫ | |||
* [[User:Michiexile/MATH198/Lecture 9]] |
* [[User:Michiexile/MATH198/Lecture 9]] |
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| + | ** Catamorphisms |
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| + | ** Anamorphisms |
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| + | ** Hylomorphisms |
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| + | ** Metamorphisms |
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| + | ** Paramorphisms |
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| + | ** Apomorphisms |
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| ⚫ | |||
* [[User:Michiexile/MATH198/Lecture 10]] |
* [[User:Michiexile/MATH198/Lecture 10]] |
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| ⚫ | |||
| − | |||
| + | ** Classifying objects |
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| − | |||
| + | ** Topoi |
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| − | |||
| ⚫ | |||
| − | Things yet to cover: |
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| − | |||
| − | Ana/Kata/Hylo/Zygo-morphism. |
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| − | |||
| − | M-algebras. |
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| − | |||
| ⚫ | |||
| − | |||
| − | Freyd's functor theorem. |
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| − | |||
| − | Adjunction properties and theorems. |
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| − | |||
| − | Examples of Adjunctions. |
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| − | |||
| − | |||
| − | ** Review. |
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| − | |||
| − | ** Topos. |
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| ⚫ | |||
| ⚫ | |||
| − | |||
| − | ** Recursion as a categorical construction. |
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| − | ** Recursive categories. |
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| − | ** Recursion as fixed points of monad algebras. |
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| − | ** Recursion using special morphisms. |
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| − | *** Hylo- |
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| − | *** Zygo- |
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| − | *** et.c. |
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| − | |||
| ⚫ | |||
| − | ** Examples of adjunctions. |
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| − | ** Things that are not adjunctions. |
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| − | |||
| − | ** Yoneda Lemma. |
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| − | *** Adjoints are unique up to isomorphism. |
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Revision as of 18:43, 17 November 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
- Monoid objects.
- Monads.
- Triples.
- Kleisli category.
- Monad factorization.
- User:Michiexile/MATH198/Lecture 8
- Algebras over monads
- Algebras over endofunctors
- Initial algebras and recursion
- Lambek's lemma
- User:Michiexile/MATH198/Lecture 9
- Catamorphisms
- Anamorphisms
- Hylomorphisms
- Metamorphisms
- Paramorphisms
- Apomorphisms
- Properties of adjunctions, examples of adjunctions
- User:Michiexile/MATH198/Lecture 10
- Power objects
- Classifying objects
- Topoi
- Internal logic