# User:Michiexile/MATH198

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** Internal language and logic. | ** Internal language and logic. | ||

* Haskell-Curry isomorphism. | * Haskell-Curry isomorphism. | ||

+ | * Recursive categories. | ||

+ | * Recursion as fixed points of monad algebras. | ||

+ | * Recursion using special morphisms. | ||

+ | ** Hylo- | ||

+ | ** Zygo- | ||

+ | ** et.c. |

## Revision as of 13:54, 18 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.

- 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.