User:Michiexile/MATH198
< User:Michiexile
Jump to navigation
Jump to search
Revision as of 22:23, 29 October 2009 by Michiexile (talk | contribs)
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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.