Mathematical Foundations Lecture Notes
As a consequence of the weekly seminars
held by the Mathematical Foundations Group we are now
beginning to make a selection of lecture notes available. This page
serves as a directory for these and gives a brief description of the contents
of each set of notes. Where there is a choice of file format, the
PostScript (ps) version is likely to be the best looking (although
they all print properly).
Sheaves
Introductory notes on the point-free approach to sheaves and $Omega$-sets from
a course given by Harold
Simmons.
Let $\Omega$ be an arbitrary frame. We then consider the category
$\Psh(\Omega)$ of presheaves on $\Omega$ and the category $\Set(\Omega)$ of
$\Omega$-sets. There are various other associated
categories and functors between them. These are described with emphasis
on the functor which separates a presheaf and the functor that
sheafifies a presheaf. (49 pages + 13 pages of solutions.)
Available in ps.gz,
pdf.gz
and
dvi.gz
format.
Game Theory
These are full notes for an introductory course in Game Theory, given by Andrea Schalk.
The notes are aimed at somebody who hasn't had any exposure to games at all
and would like a detailed description of the various constructions, complete
with pictures. (49 pages.)
Available in ps.gz or
pdf format.
Monads
Notes from a short introduction to monads given by Andrea Schalk. It
motivates the definition, makes the connection to Kleisli triples and
then proceeds to explain the Kleisli category and the category of
Eilenberg-Moore algebras for a monad. It assumes that the reader is
familiar with category theory up to adjunctions. (16 pages.)
Available in ps.gz or
pdf format.
Other Relevant Links
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These pages are maintained by Don MacInnes. Last changed on
4th October 2004.
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