User:Michiexile/MATH198
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Michiexile (Talk  contribs) 
Michiexile (Talk  contribs) 

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* [[User:Michiexile/MATH198/Lecture 4]] 
* [[User:Michiexile/MATH198/Lecture 4]] 

−  ** The power of dualization. 

−  ** Limits, colimits. 

** Products, coproducts. 
** Products, coproducts. 

−  ** Equalizers, coequalizers. 
+  ** The power of dualization. 
+  ** The algebra of datatypes 

+  
* [[User:Michiexile/MATH198/Lecture 5]] 
* [[User:Michiexile/MATH198/Lecture 5]] 

+  ** Limits, colimits. 

+  ** Equalizers, coequalizers. 

+  ** Simulation using test suites. 

+  
+  * [[User:Michiexile/MATH198/Lecture 6]] 

** Adjunctions. 
** Adjunctions. 

** Free and forgetful. 
** Free and forgetful. 

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

** Monads. 
** Monads. 

** Triples. 
** Triples. 

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** Monad factorization. 
** Monad factorization. 

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

−  * [[User:Michiexile/MATH198/Lecture 7]] 

** Recursion as a categorical construction. 
** Recursion as a categorical construction. 

** Recursive categories. 
** Recursive categories. 

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*** et.c. 
*** et.c. 

−  * [[User:Michiexile/MATH198/Lecture 8]] 
+  * [[User:Michiexile/MATH198/Lecture 9]] 
** Topos. 
** Topos. 

** Exponentials. 
** Exponentials. 

** Power objects. 
** Power objects. 

** Cartesian Closed Categories. 
** Cartesian Closed Categories. 

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

** Internal logic. 
** Internal logic. 

Revision as of 01:17, 8 October 2009
Course overview
Page is work in progress for background material for the Fall 2009 lecture course MATH198[1] on Category Theory and Functional Programming that I am planning to give 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.
 Equalizers, coequalizers.
 Simulation using test suites.
 User:Michiexile/MATH198/Lecture 6
 Adjunctions.
 Free and forgetful.
 User:Michiexile/MATH198/Lecture 7
 Monoid objects.
 Monads.
 Triples.
 The Kleisli category.
 Monad factorization.
 User:Michiexile/MATH198/Lecture 8
 Recursion as a categorical construction.
 Recursive categories.
 Recursion as fixed points of monad algebras.
 Recursion using special morphisms.
 Hylo
 Zygo
 et.c.
 User:Michiexile/MATH198/Lecture 9
 Topos.
 Exponentials.
 Power objects.
 Cartesian Closed Categories.
 Internal logic.