User:Michiexile/MATH198

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Revision as of 22:11, 21 October 2009 (edit) Michiexile (Talk | contribs) ← Previous diff		Revision as of 21:02, 28 October 2009 (edit) (undo) Michiexile (Talk | contribs) Next diff →
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	* [[User:Michiexile/MATH198/Lecture 5]]		* [[User:Michiexile/MATH198/Lecture 5]]
	** Limits, colimits.		** Limits, colimits.
-	** Equalizers, coequalizers.
-	** Simulation using test suites.
	* [[User:Michiexile/MATH198/Lecture 6]]		* [[User:Michiexile/MATH198/Lecture 6]]
		+	** Equalizers, coequalizers.
	** Pushouts/pullbacks		** Pushouts/pullbacks
	** Adjunctions.		** Adjunctions.
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	** Monads.		** Monads.
	** Triples.		** Triples.
-	** The Kleisli category.	+	** Kleisli category.
	** Monad factorization.		** Monad factorization.
	* [[User:Michiexile/MATH198/Lecture 8]]		* [[User:Michiexile/MATH198/Lecture 8]]
-	** Recursion as a categorical construction.	+	** Properties of adjunctions.
-	** Recursive categories.	+	** Examples of adjunctions.
-	** Recursion as fixed points of monad algebras.	+	** Things that are not adjunctions.
-	** Recursion using special morphisms.	+
-	*** Hylo-	+
-	*** Zygo-	+
-	*** et.c.	+
	* [[User:Michiexile/MATH198/Lecture 9]]		* [[User:Michiexile/MATH198/Lecture 9]]
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	* [[User:Michiexile/MATH198/Lecture 10]]		* [[User:Michiexile/MATH198/Lecture 10]]
	** Review.		** Review.
		+
		+	** Recursion as a categorical construction.
		+	** Recursive categories.
		+	** Recursion as fixed points of monad algebras.
		+	** Recursion using special morphisms.
		+	*** Hylo-
		+	*** Zygo-
		+	*** et.c.

---

Revision as of 21:02, 28 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
  • 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
  • Properties of adjunctions.
  • Examples of adjunctions.
  • Things that are not adjunctions.

• User:Michiexile/MATH198/Lecture 9
  • Topos.
  • Exponentials.
  • Power objects.
  • Cartesian Closed Categories.
  • Internal logic.

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

• • Recursion as a categorical construction.
  • Recursive categories.
  • Recursion as fixed points of monad algebras.
  • Recursion using special morphisms.
    • Hylo-
    • Zygo-
    • et.c.