User:Michiexile/MATH198

Course overview

Page is work in progress for background material for the Fall 2009 lecture course on Category Theory with a view towards applications that I am planning to give at Stanford University.

Single unit course. 10 lectures.

• Functors.
• Natural transformations.
• Category of categories.
• The power of dualization.
• Limits, colimits.
• Products, coproducts.
• Equalizers, coequalizers.
• Exponentials.
• Power objects.
• Monads.
• Monoids.
• Triples.
• Cartesian Closed Categories.
  • Categorical logic.
• Topoi.
  • Internal language and logic.
• Haskell-Curry 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.
  • Concrete categories.
    • Set.
    • Various categories capturing linear algebra.
  • Small categories.
    • Partial orders.
    • Monoids.
    • Finite groups.
  • Special morphisms
    • Epimorphism.
    • Monomorphism.
    • Isomorphism.
    • Endomorphism.
    • Automorphism.
  • Special objects
    • Initial.
    • Terminal.
    • Null.

• User:Michiexile/SU09 Lecture 2

• User:Michiexile/SU09 Lecture 3

• User:Michiexile/SU09 Lecture 4

• User:Michiexile/SU09 Lecture 5

• User:Michiexile/SU09 Lecture 6

• User:Michiexile/SU09 Lecture 7

• User:Michiexile/SU09 Lecture 8

• User:Michiexile/SU09 Lecture 9

• User:Michiexile/SU09 Lecture 10