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Single unit course. 10 lectures.
 
Single unit course. 10 lectures.
   
* Category: Definition and examples.
 
* Concrete categories.
 
** Set.
 
** Various categories capturing linear algebra.
 
* Small categories.
 
** Partial orders.
 
** Monoids.
 
** Finite groups.
 
* Special morphisms
 
** Epimorphism.
 
** Monomorphism.
 
** Isomorphism.
 
** Endomorphism.
 
** Automorphism.
 
* Special objects
 
** Initial.
 
** Terminal.
 
** Null.
 
 
* Functors.
 
* Functors.
 
* Natural transformations.
 
* Natural transformations.
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* [[User:Michiexile/SU09 Lecture 1]]
 
* [[User:Michiexile/SU09 Lecture 1]]
  +
** Category: Definition and examples.
  +
** Concrete categories.
  +
*** Set.
  +
*** Various categories capturing linear algebra.
  +
** Small categories.
  +
*** Partial orders.
  +
*** Monoids.
  +
*** Finite groups.
  +
** Special morphisms
  +
*** Epimorphism.
  +
*** Monomorphism.
  +
*** Isomorphism.
  +
*** Endomorphism.
  +
*** Automorphism.
  +
** Special objects
  +
*** Initial.
  +
*** Terminal.
  +
*** Null.
  +
 
* [[User:Michiexile/SU09 Lecture 2]]
 
* [[User:Michiexile/SU09 Lecture 2]]
  +
 
* [[User:Michiexile/SU09 Lecture 3]]
 
* [[User:Michiexile/SU09 Lecture 3]]
  +
 
* [[User:Michiexile/SU09 Lecture 4]]
 
* [[User:Michiexile/SU09 Lecture 4]]
  +
 
* [[User:Michiexile/SU09 Lecture 5]]
 
* [[User:Michiexile/SU09 Lecture 5]]
  +
 
* [[User:Michiexile/SU09 Lecture 6]]
 
* [[User:Michiexile/SU09 Lecture 6]]
  +
 
* [[User:Michiexile/SU09 Lecture 7]]
 
* [[User:Michiexile/SU09 Lecture 7]]
  +
 
* [[User:Michiexile/SU09 Lecture 8]]
 
* [[User:Michiexile/SU09 Lecture 8]]
  +
 
* [[User:Michiexile/SU09 Lecture 9]]
 
* [[User:Michiexile/SU09 Lecture 9]]
  +
 
* [[User:Michiexile/SU09 Lecture 10]]
 
* [[User:Michiexile/SU09 Lecture 10]]

Revision as of 11:53, 27 August 2009

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.

Single unit course. 10 lectures.

  • Functors.
  • Natural transformations.
  • Category of categories.
  • The power of dualization.
  • Limits, colimits.
  • Products, coproducts.
  • Equalizers, coequalizers.
  • Exponentials.
  • Power objects.
  • Monads.
  • Monoids.
  • Triples.
  • 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.
    • Special morphisms
      • Epimorphism.
      • Monomorphism.
      • Isomorphism.
      • Endomorphism.
      • Automorphism.
    • Special objects
      • Initial.
      • Terminal.
      • Null.