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User:Michiexile/MATH198

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* [[User:Michiexile/MATH198/Lecture 8]]
 
* [[User:Michiexile/MATH198/Lecture 8]]
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** Algebras over monads
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** Algebras over endofunctors
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** Initial algebras and recursion
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** Lambek's lemma
   
 
* [[User:Michiexile/MATH198/Lecture 9]]
 
* [[User:Michiexile/MATH198/Lecture 9]]
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** Catamorphisms
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** Anamorphisms
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** Hylomorphisms
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** Metamorphisms
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** Paramorphisms
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** Apomorphisms
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** Properties of adjunctions, examples of adjunctions
   
 
* [[User:Michiexile/MATH198/Lecture 10]]
 
* [[User:Michiexile/MATH198/Lecture 10]]
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** Power objects
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** Classifying objects
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** Topoi
Things yet to cover:
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** Internal logic
 
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.
 

Revision as of 18:43, 17 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.




  • User:Michiexile/MATH198/Lecture 9
    • Catamorphisms
    • Anamorphisms
    • Hylomorphisms
    • Metamorphisms
    • Paramorphisms
    • Apomorphisms
    • Properties of adjunctions, examples of adjunctions