User:Michiexile/MATH198
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Single unit course. 10 lectures. | Single unit course. 10 lectures. | ||
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* Functors. | * Functors. | ||
* Natural transformations. | * Natural transformations. | ||
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* [[User:Michiexile/SU09 Lecture 1]] | * [[User:Michiexile/SU09 Lecture 1]] | ||
| + | ** Category: Definition and examples. | ||
| + | ** Concrete categories. | ||
| + | *** Set. | ||
| + | *** Various categories capturing linear algebra. | ||
| + | ** Small categories. | ||
| + | *** Partial orders. | ||
| + | *** Monoids. | ||
| + | *** Finite groups. | ||
| + | ** Special morphisms | ||
| + | *** Epimorphism. | ||
| + | *** Monomorphism. | ||
| + | *** Isomorphism. | ||
| + | *** Endomorphism. | ||
| + | *** Automorphism. | ||
| + | ** Special objects | ||
| + | *** Initial. | ||
| + | *** Terminal. | ||
| + | *** Null. | ||
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* [[User:Michiexile/SU09 Lecture 2]] | * [[User:Michiexile/SU09 Lecture 2]] | ||
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* [[User:Michiexile/SU09 Lecture 3]] | * [[User:Michiexile/SU09 Lecture 3]] | ||
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* [[User:Michiexile/SU09 Lecture 4]] | * [[User:Michiexile/SU09 Lecture 4]] | ||
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* [[User:Michiexile/SU09 Lecture 5]] | * [[User:Michiexile/SU09 Lecture 5]] | ||
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* [[User:Michiexile/SU09 Lecture 6]] | * [[User:Michiexile/SU09 Lecture 6]] | ||
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* [[User:Michiexile/SU09 Lecture 7]] | * [[User:Michiexile/SU09 Lecture 7]] | ||
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* [[User:Michiexile/SU09 Lecture 8]] | * [[User:Michiexile/SU09 Lecture 8]] | ||
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* [[User:Michiexile/SU09 Lecture 9]] | * [[User:Michiexile/SU09 Lecture 9]] | ||
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* [[User:Michiexile/SU09 Lecture 10]] | * [[User:Michiexile/SU09 Lecture 10]] | ||
Revision as of 11:53, 27 August 2009
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.
- 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.
- User:Michiexile/SU09 Lecture 1
- Category: Definition and examples.
- Concrete categories.
- Set.
- Various categories capturing linear algebra.
- Small categories.
- Partial orders.
- Monoids.
- Finite groups.
- Special morphisms
- Epimorphism.
- Monomorphism.
- Isomorphism.
- Endomorphism.
- Automorphism.
- Special objects
- Initial.
- Terminal.
- Null.
