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User:Michiexile/MATH198

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Single unit course. 10 lectures. Each lecture is Wednesday 4.15-5.05 in 380F.
 
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]]
 
* [[User:Michiexile/SU09 Lecture 1]]
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*** Monoids.
 
*** Monoids.
 
*** Finite groups.
 
*** Finite groups.
  +
** Haskell-Curry isomorphism.
   
   
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* [[User:Michiexile/SU09 Lecture 7]]
 
* [[User:Michiexile/SU09 Lecture 7]]
 
** Recursion as a categorical construction.
 
** Recursion as a categorical construction.
  +
** Recursive categories.
  +
** Recursion as fixed points of monad algebras.
  +
** Recursion using special morphisms.
  +
*** Hylo-
  +
*** Zygo-
  +
*** et.c.
   
 
* [[User:Michiexile/SU09 Lecture 8]]
 
* [[User:Michiexile/SU09 Lecture 8]]
 
** Topos.
 
** Topos.
  +
** Exponentials.
  +
** Power objects.
  +
** Cartesian Closed Categories.
   
 
* [[User:Michiexile/SU09 Lecture 9]]
 
* [[User:Michiexile/SU09 Lecture 9]]

Revision as of 12:44, 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.


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


  • User:Michiexile/SU09 Lecture 7
    • Recursion as a categorical construction.
    • Recursive categories.
    • Recursion as fixed points of monad algebras.
    • Recursion using special morphisms.
      • Hylo-
      • Zygo-
      • et.c.