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* [[User:Michiexile/MATH198/Lecture 7]]
 
* [[User:Michiexile/MATH198/Lecture 7]]
** Properties of adjunctions.
 
** Examples of adjunctions.
 
** Things that are not adjunctions.
 
 
* [[User:Michiexile/MATH198/Lecture 8]]
 
 
** Monoid objects.
 
** Monoid objects.
 
** Monads.
 
** Monads.
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** Kleisli category.
 
** Kleisli category.
 
** Monad factorization.
 
** Monad factorization.
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* [[User:Michiexile/MATH198/Lecture 8]]
   
 
* [[User:Michiexile/MATH198/Lecture 9]]
 
* [[User:Michiexile/MATH198/Lecture 9]]
** Yoneda Lemma.
 
*** Adjoints are unique up to isomorphism.
 
   
 
* [[User:Michiexile/MATH198/Lecture 10]]
 
* [[User:Michiexile/MATH198/Lecture 10]]
  +
  +
  +
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Things yet to cover:
  +
  +
Ana/Kata/Hylo/Zygo-morphism.
  +
  +
M-algebras.
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  +
Yoneda's lemma.
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  +
Freyd's functor theorem.
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  +
Adjunction properties and theorems.
  +
  +
Examples of Adjunctions.
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** Review.
 
** Review.
   
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*** Zygo-
 
*** Zygo-
 
*** et.c.
 
*** et.c.
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  +
** Properties of adjunctions.
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** Examples of adjunctions.
  +
** Things that are not adjunctions.
  +
  +
** Yoneda Lemma.
  +
*** Adjoints are unique up to isomorphism.

Revision as of 15:21, 10 November 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.





Things yet to cover:

Ana/Kata/Hylo/Zygo-morphism.

M-algebras.

Yoneda's lemma.

Freyd's functor theorem.

Adjunction properties and theorems.

Examples of Adjunctions.


    • Review.
    • 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.
    • Properties of adjunctions.
    • Examples of adjunctions.
    • Things that are not adjunctions.
    • Yoneda Lemma.
      • Adjoints are unique up to isomorphism.