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 MATH198[http://coursework.stanford.edu/homepage/F09/F09MATH19801.html] on Category Theory and Functional Programming 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. 

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

+  ** Algebras over monads 

+  ** Algebras over endofunctors 

+  ** Initial algebras and recursion 

+  ** Lambek's lemma 

* [[User:Michiexile/MATH198/Lecture 9]] 
* [[User:Michiexile/MATH198/Lecture 9]] 

+  ** Catamorphisms 

+  ** Anamorphisms 

+  ** Hylomorphisms 

+  ** Metamorphisms 

+  ** Paramorphisms 

+  ** Apomorphisms 

+  ** Properties of adjunctions, examples of adjunctions 

* [[User:Michiexile/MATH198/Lecture 10]] 
* [[User:Michiexile/MATH198/Lecture 10]] 

−  +  ** Power objects 

−  +  ** Classifying objects 

−  +  ** Topoi 

−  Things yet to cover: 
+  ** Internal logic 
−  
−  Ana/Kata/Hylo/Zygomorphism. 

−  
−  Malgebras. 

−  
−  Yoneda's lemma. 

−  
−  Freyd's functor theorem. 

−  
−  Adjunction properties and theorems. 

−  
−  Examples of Adjunctions. 

−  
−  
−  ** Review. 

−  
−  ** Topos. 

−  ** Power objects. 

−  ** Internal logic. 

−  
−  ** Recursion as a categorical construction. 

−  ** Recursive categories. 

−  ** Recursion as fixed points of monad algebras. 

−  ** Recursion using special morphisms. 

−  *** Hylo 

−  *** Zygo 

−  *** et.c. 

−  
−  ** Properties of adjunctions. 

−  ** Examples of adjunctions. 

−  ** Things that are not adjunctions. 

−  
−  ** Yoneda Lemma. 

−  *** Adjoints are unique up to isomorphism. 
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