User:Michiexile/MATH198

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	** Functors.		** Functors.
	** Category of categories.		** Category of categories.
-
-	* [[User:Michiexile/MATH198/Lecture 4]]
	** Natural transformations.		** Natural transformations.
-	** Adjunctions.
-	** Free and forgetful.
-	* [[User:Michiexile/MATH198/Lecture 5]]	+	* [[User:Michiexile/MATH198/Lecture 4]]
	** The power of dualization.		** The power of dualization.
	** Limits, colimits.		** Limits, colimits.
	** Products, coproducts.		** Products, coproducts.
	** Equalizers, coequalizers.		** Equalizers, coequalizers.
		+
		+	* [[User:Michiexile/MATH198/Lecture 5]]
		+	** Adjunctions.
		+	** Free and forgetful.
	* [[User:Michiexile/MATH198/Lecture 6]]		* [[User:Michiexile/MATH198/Lecture 6]]

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Revision as of 23:15, 6 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 4.15-5.05 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 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
  • The power of dualization.
  • Limits, colimits.
  • Products, coproducts.
  • Equalizers, coequalizers.

• User:Michiexile/MATH198/Lecture 5
  • Adjunctions.
  • Free and forgetful.

• User:Michiexile/MATH198/Lecture 6
  • Monoids.
  • Monads.
  • Triples.
  • The Kleisli category.
  • Monad factorization.

• User:Michiexile/MATH198/Lecture 7
  • 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 8
  • Topos.
  • Exponentials.
  • Power objects.
  • Cartesian Closed Categories.

• User:Michiexile/MATH198/Lecture 9
  • Internal logic.

• User:Michiexile/MATH198/Lecture 10
  • Review.