User:Michiexile/MATH198
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==Course overview== | ==Course overview== | ||
| - | Page is | + | Page is the background material for the Fall 2009 lecture course MATH198[http://coursework.stanford.edu/homepage/F09/F09-MATH-198-01.html] on Category Theory and Functional Programming that I gave at Stanford University. |
Single unit course. 10 lectures. Each lecture is Wednesday 4.15-5.05 in 380F. | Single unit course. 10 lectures. Each lecture is Wednesday 4.15-5.05 in 380F. | ||
| Line 43: | Line 43: | ||
* [[User:Michiexile/MATH198/Lecture 5]] | * [[User:Michiexile/MATH198/Lecture 5]] | ||
** Limits, colimits. | ** Limits, colimits. | ||
| - | |||
| - | |||
* [[User:Michiexile/MATH198/Lecture 6]] | * [[User:Michiexile/MATH198/Lecture 6]] | ||
| + | ** Equalizers, coequalizers. | ||
| + | ** Pushouts/pullbacks | ||
** Adjunctions. | ** Adjunctions. | ||
** Free and forgetful. | ** Free and forgetful. | ||
| Line 55: | Line 55: | ||
** Monads. | ** Monads. | ||
** Triples. | ** Triples. | ||
| - | ** | + | ** Kleisli category. |
** Monad factorization. | ** Monad factorization. | ||
* [[User:Michiexile/MATH198/Lecture 8]] | * [[User:Michiexile/MATH198/Lecture 8]] | ||
| - | ** | + | ** Algebras over monads |
| - | ** | + | ** Algebras over endofunctors |
| - | ** | + | ** Initial algebras and recursion |
| - | ** | + | ** Lambek's lemma |
| - | + | ||
| - | + | ||
| - | + | ||
* [[User:Michiexile/MATH198/Lecture 9]] | * [[User:Michiexile/MATH198/Lecture 9]] | ||
| - | ** | + | ** Catamorphisms |
| - | ** | + | ** Anamorphisms |
| - | ** | + | ** Hylomorphisms |
| - | ** | + | ** Metamorphisms |
| - | ** | + | ** Paramorphisms |
| + | ** Apomorphisms | ||
| + | ** Properties of adjunctions, examples of adjunctions | ||
* [[User:Michiexile/MATH198/Lecture 10]] | * [[User:Michiexile/MATH198/Lecture 10]] | ||
| - | ** | + | ** Power objects |
| + | ** Classifying objects | ||
| + | ** Topoi | ||
| + | ** Internal logic | ||
Current revision
Course overview
Page is the background material for the Fall 2009 lecture course MATH198[1] on Category Theory and Functional Programming that I gave 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
