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                   A First Course in Category Theory
                          by Jaap van Ooosten

  Jaap van Oosten has written a first course in category theory which 
is intende to contain what's presumed knowledge in not too specialized
papers and theses (in computer science). It's 75 pages long.
The synopsis is:

 1. Categories and functors. Definitions and examples. Duality.
 2. Natural transformations. Exponents in Cat. Yoneda lemma. Equivalent
    categories; Set^op equivalent to Complete Atomic Boolean Algebras.
 3. Limits and Colimits. Functors preserving (reflecting) them. 
    (Finitely) complete categories. Limits by products and equalizers.
 4. A little categorical logic. Regular categories, regular epi-mono
    factorization, subobjects. Interpretation of coherent logic in 
    regular categories. Expressing categorical facts in the logic. 
    Example of \Omega -valued sets for a frame \Omega.
 5. Adjunctions. Examples. (Co)limits as adjoints. Adjoints preserve 
    (co)limits.  Adjoint functor theorem.
 6. Monads and Algebras. Examples. Eilenberg Moore and Kleisli as 
    terminal and initial adjunctions inducing a monad. Groups monadic 
    over Set.  Lift and Powerset monads and their algebras. Forgetful 
    functor from T-Alg creates limits.
 7. Cartesian closed categories and the \lambda-calculus. Examples of 
    ccc's.  Parameter theorem. Typed \lambda calculus and its 
    interpretation in ccc's. Ccc's with natural numbers object: all 
    primitive recursive functions are representable.

  The notes are available by anonymous ftp from URL:
ftp://ftp.daimi.aau.dk/pub/BRICS/LS/95/1/BRICS-LS-95-1.ps.gz