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User:Michiexile/MATH198

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* [[User:Michiexile/MATH198/Lecture 7]]
 
* [[User:Michiexile/MATH198/Lecture 7]]
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** Properties of adjunctions.
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** Examples of adjunctions.
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** Things that are not adjunctions.
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* [[User:Michiexile/MATH198/Lecture 8]]
 
** Monoid objects.
 
** Monoid objects.
 
** Monads.
 
** Monads.
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** Kleisli category.
 
** Kleisli category.
 
** Monad factorization.
 
** Monad factorization.
 
* [[User:Michiexile/MATH198/Lecture 8]]
 
** Properties of adjunctions.
 
** Examples of adjunctions.
 
** Things that are not adjunctions.
 
   
 
* [[User:Michiexile/MATH198/Lecture 9]]
 
* [[User:Michiexile/MATH198/Lecture 9]]
** Topos.
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** Yoneda Lemma.
** Exponentials.
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*** Adjoints are unique up to isomorphism.
** Power objects.
 
** Cartesian Closed Categories.
 
** Internal logic.
 
   
 
* [[User:Michiexile/MATH198/Lecture 10]]
 
* [[User:Michiexile/MATH198/Lecture 10]]
 
** Review.
 
** Review.
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** Topos.
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** Power objects.
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** Internal logic.
   
 
** Recursion as a categorical construction.
 
** Recursion as a categorical construction.

Revision as of 22:23, 29 October 2009

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.




    • 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.