Difference between revisions of "User:Michiexile/MATH198"

From HaskellWiki
Jump to navigation Jump to search
 
(15 intermediate revisions by the same user not shown)
Line 1: Line 1:
 
==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.
 +
Page is the background material for the Fall 2009 lecture course MATH198[http://coursework.stanford.edu/homepage/F09/F09-MATH-198-01.html] on Category Theory and Functional Programming that I gave at Stanford University.
   
−
Single unit course. 10 lectures.
 +
Single unit course. 10 lectures. Each lecture is Wednesday 4.15-5.05 in 380F.
   
−
* 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.
  
−
* 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]]
 +
* [[User:Michiexile/MATH198/Lecture 1]]
  +
** Category: Definition and examples.
−
* [[User:Michiexile/SU09 Lecture 2]]
  
  +
** Concrete categories.
−
* [[User:Michiexile/SU09 Lecture 3]]
  
  +
*** Set.
−
* [[User:Michiexile/SU09 Lecture 4]]
  
  +
*** Various categories capturing linear algebra.
−
* [[User:Michiexile/SU09 Lecture 5]]
  
  +
** Small categories.
−
* [[User:Michiexile/SU09 Lecture 6]]
  
  +
*** Partial orders.
−
* [[User:Michiexile/SU09 Lecture 7]]
  
  +
*** Monoids.
−
* [[User:Michiexile/SU09 Lecture 8]]
  
  +
*** Finite groups.
−
* [[User:Michiexile/SU09 Lecture 9]]
  
  +
** Haskell-Curry isomorphism.
−
* [[User:Michiexile/SU09 Lecture 10]]
  
  +
  +
  +
* [[User:Michiexile/MATH198/Lecture 2]]
  +
** Special morphisms
  +
*** Epimorphism.
  +
*** Monomorphism.
  +
*** Isomorphism.
  +
*** Endomorphism.
  +
*** Automorphism.
  +
** Special objects
  +
*** Initial.
  +
*** Terminal.
  +
*** Null.
  +
  +
* [[User:Michiexile/MATH198/Lecture 3]]
  +
** Functors.
  +
** Category of categories.
  +
** Natural transformations.
  +
  +
* [[User:Michiexile/MATH198/Lecture 4]]
  +
** Products, coproducts.
  +
** The power of dualization.
  +
** The algebra of datatypes
  +
  +
  +
* [[User:Michiexile/MATH198/Lecture 5]]
  +
** Limits, colimits.
  +
  +
* [[User:Michiexile/MATH198/Lecture 6]]
  +
** Equalizers, coequalizers.
  +
** Pushouts/pullbacks
  +
** Adjunctions.
  +
** Free and forgetful.
  +
  +
  +
* [[User:Michiexile/MATH198/Lecture 7]]
  +
** Monoid objects.
  +
** Monads.
  +
** Triples.
  +
** Kleisli category.
  +
** Monad factorization.
  +
  +
* [[User:Michiexile/MATH198/Lecture 8]]
  +
** Algebras over monads
  +
** Algebras over endofunctors
  +
** Initial algebras and recursion
  +
** Lambek's lemma
  +
  +
* [[User:Michiexile/MATH198/Lecture 9]]
  +
** Catamorphisms
  +
** Anamorphisms
  +
** Hylomorphisms
  +
** Metamorphisms
  +
** Paramorphisms
  +
** Apomorphisms
  +
** Properties of adjunctions, examples of adjunctions
  +
  +
* [[User:Michiexile/MATH198/Lecture 10]]
  +
** Power objects
  +
** Classifying objects
  +
** Topoi
  +
** Internal logic

Latest revision as of 05:51, 24 July 2010

Course overview

Page is the background material for the Fall 2009 lecture course MATH198[1] on Category Theory and Functional Programming that I gave 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
Retrieved from "https://wiki.haskell.org/index.php?title=User:Michiexile/MATH198&oldid=36339"