User:Michiexile/MATH198
From HaskellWiki
< User:Michiexile(Difference between revisions)
Michiexile (Talk  contribs) 
Michiexile (Talk  contribs) 

(13 intermediate revisions by one 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 MATH198 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/F09MATH19801.html] on Category Theory and Functional Programming that I gave at Stanford University. 
Single unit course. 10 lectures. Each lecture is Wednesday 4.155.05 in 380F. 
Single unit course. 10 lectures. Each lecture is Wednesday 4.155.05 in 380F. 

−  * Exponentials. 
+  * [[User:Michiexile/MATH198/Lecture 1]] 
−  * Power objects. 

−  * Cartesian Closed Categories. 

−  ** Categorical logic. 

−  * Topoi. 

−  ** Internal language and logic. 

−  * HaskellCurry 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. 
** Category: Definition and examples. 

** Concrete categories. 
** Concrete categories. 

Line 15:  Line 15:  
*** Monoids. 
*** Monoids. 

*** Finite groups. 
*** Finite groups. 

+  ** HaskellCurry isomorphism. 

−  * [[User:Michiexile/SU09 Lecture 2]] 
+  * [[User:Michiexile/MATH198/Lecture 2]] 
** Special morphisms 
** Special morphisms 

*** Epimorphism. 
*** Epimorphism. 

Line 29:  Line 30:  
*** Null. 
*** Null. 

−  * [[User:Michiexile/SU09 Lecture 3]] 
+  * [[User:Michiexile/MATH198/Lecture 3]] 
** Functors. 
** Functors. 

+  ** Category of categories. 

** Natural transformations. 
** Natural transformations. 

−  ** Category of categories. 

−  * [[User:Michiexile/SU09 Lecture 4]] 
+  * [[User:Michiexile/MATH198/Lecture 4]] 
−  ** Adjunctions. 
+  ** Products, coproducts. 
−  ** Free and forgetful. 
+  ** The power of dualization. 
+  ** The algebra of datatypes 

+  
−  * [[User:Michiexile/SU09 Lecture 5]] 
+  * [[User:Michiexile/MATH198/Lecture 5]] 
−  ** The power of dualization. 

** Limits, colimits. 
** Limits, colimits. 

−  ** Products, coproducts. 
+  
+  * [[User:Michiexile/MATH198/Lecture 6]] 

** Equalizers, coequalizers. 
** Equalizers, coequalizers. 

+  ** Pushouts/pullbacks 

+  ** Adjunctions. 

+  ** Free and forgetful. 

−  * [[User:Michiexile/SU09 Lecture 6]] 
+  
−  ** Monoids. 
+  * [[User:Michiexile/MATH198/Lecture 7]] 
+  ** Monoid objects. 

** Monads. 
** Monads. 

** Triples. 
** Triples. 

−  ** The Kleisli category. 
+  ** Kleisli category. 
** Monad factorization. 
** Monad factorization. 

+  * [[User:Michiexile/MATH198/Lecture 8]] 

+  ** Algebras over monads 

+  ** Algebras over endofunctors 

+  ** Initial algebras and recursion 

+  ** Lambek's lemma 

−  * [[User:Michiexile/SU09 Lecture 7]] 
+  * [[User:Michiexile/MATH198/Lecture 9]] 
−  ** Recursion as a categorical construction. 
+  ** Catamorphisms 
−  +  ** Anamorphisms 

−  * [[User:Michiexile/SU09 Lecture 8]] 
+  ** Hylomorphisms 
−  ** Topos. 
+  ** Metamorphisms 
−  +  ** Paramorphisms 

−  * [[User:Michiexile/SU09 Lecture 9]] 
+  ** Apomorphisms 
−  ** Internal logic. 
+  ** Properties of adjunctions, examples of adjunctions 
−  * [[User:Michiexile/SU09 Lecture 10]] 
+  * [[User:Michiexile/MATH198/Lecture 10]] 
−  ** Review. 
+  ** Power objects 
+  ** Classifying objects 

+  ** Topoi 

+  ** Internal logic 
Latest revision as of 05:51, 24 July 2010
[edit] 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 4.155.05 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.
 HaskellCurry isomorphism.
 User:Michiexile/MATH198/Lecture 2
 Special morphisms
 Epimorphism.
 Monomorphism.
 Isomorphism.
 Endomorphism.
 Automorphism.
 Special objects
 Initial.
 Terminal.
 Null.
 Special morphisms
 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