User:Michiexile/MATH198
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Course overview
Page is work in progress for background material for the Fall 2009 lecture course on Category Theory with a view towards applications that I am planning to give at Stanford University.
Single unit course. 10 lectures.
- Category: Definition and examples.
- Concrete categories.
- Set.
- Various categories capturing linear algebra.
- Small categories.
- Partial orders.
- Finite groups.
- Special morphisms
- Epimorphism.
- Monomorphism.
- Isomorphism.
- Endomorphism.
- Automorphism.
- Special objects
- Initial.
- Terminal.
- Null.
- Functors.
- Natural transformations.
- Category of categories.
- The power of dualization.
- Limits, colimits.
- Products, coproducts.
- Equalizers, coequalizers.
- Exponentials.
- Power objects.
- Monads.
- Monoids.
- Triples.
- Cartesian Closed Categories.
- Categorical logic.
- Topoi.
- Internal language and logic.
- Haskell-Curry isomorphism.
- Recursive categories.
- Recursion as fixed points of monad algebras.
- Recursion using special morphisms.
- Hylo-
- Zygo-
- et.c.