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User:Michiexile/MATH198

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==Course overview==
 
==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.
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Page is work in progress for background material for the Fall 2009 lecture course MATH198 on Category Theory with a view towards applications that I am planning to give at Stanford University.
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 +
Single unit course. 10 lectures. Each lecture is Wednesday 4.15-5.05 in 380F.
  
Single unit course. 10 lectures.
 
  
* Functors.
 
* Natural transformations.
 
* Category of categories.
 
* The power of dualization.
 
* Limits, colimits.
 
* Products, coproducts.
 
* Equalizers, coequalizers.
 
 
* Exponentials.
 
* Exponentials.
 
* Power objects.
 
* Power objects.
* Monads.
 
* Monoids.
 
* Triples.
 
 
* Cartesian Closed Categories.
 
* Cartesian Closed Categories.
 
** Categorical logic.
 
** Categorical logic.
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*** Monoids.
 
*** Monoids.
 
*** Finite groups.
 
*** Finite groups.
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* [[User:Michiexile/SU09 Lecture 2]]
 
** Special morphisms
 
** Special morphisms
 
*** Epimorphism.
 
*** Epimorphism.
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*** Terminal.  
 
*** Terminal.  
 
*** Null.
 
*** Null.
 
* [[User:Michiexile/SU09 Lecture 2]]
 
  
 
* [[User:Michiexile/SU09 Lecture 3]]
 
* [[User:Michiexile/SU09 Lecture 3]]
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** Functors.
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** Natural transformations.
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** Category of categories.
  
 
* [[User:Michiexile/SU09 Lecture 4]]
 
* [[User:Michiexile/SU09 Lecture 4]]
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** Adjunctions.
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** Free and forgetful.
  
 
* [[User:Michiexile/SU09 Lecture 5]]
 
* [[User:Michiexile/SU09 Lecture 5]]
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** The power of dualization.
 +
** Limits, colimits.
 +
** Products, coproducts.
 +
** Equalizers, coequalizers.
  
 
* [[User:Michiexile/SU09 Lecture 6]]
 
* [[User:Michiexile/SU09 Lecture 6]]
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** Monoids.
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** Monads.
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** Triples.
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** The Kleisli category.
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** Monad factorization.
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* [[User:Michiexile/SU09 Lecture 7]]
 
* [[User:Michiexile/SU09 Lecture 7]]
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** Recursion as a categorical construction.
  
 
* [[User:Michiexile/SU09 Lecture 8]]
 
* [[User:Michiexile/SU09 Lecture 8]]
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** Topos.
  
 
* [[User:Michiexile/SU09 Lecture 9]]
 
* [[User:Michiexile/SU09 Lecture 9]]
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** Internal logic.
  
 
* [[User:Michiexile/SU09 Lecture 10]]
 
* [[User:Michiexile/SU09 Lecture 10]]
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** Review.

Revision as of 12:43, 3 September 2009

Course overview

Page is work in progress for background material for the Fall 2009 lecture course MATH198 on Category Theory with a view towards applications that I am planning to give at Stanford University.

Single unit course. 10 lectures. Each lecture is Wednesday 4.15-5.05 in 380F.


  • Exponentials.
  • Power objects.
  • 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.


  • User:Michiexile/SU09 Lecture 2
    • Special morphisms
      • Epimorphism.
      • Monomorphism.
      • Isomorphism.
      • Endomorphism.
      • Automorphism.
    • Special objects
      • Initial.
      • Terminal.
      • Null.