I am scheduled to give two tutorial
lectures. Below you will find drafts of the lectures as well as more
detailed supporting notes.
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Prologue 1
Lecture 1
Sunday at 10.30.
A primer on inverse
semigroups (Draft).
In this talk, I shall explain how inverse semigroups arose as the
abstract versions of pseudogroups of transformations, in much the same
way that groups arose as the abstract versions of transformation
groups. I shall also explain in what way inverse semigroups can be
viewed as extensions of presheaves of groups by pseudogroups. In fact,
the lecture will centre on two representations: the Wagner-Preston
representation and the Munn representation. I shall also describe the
way in which inverse semigroups can be naturally viewed as special
kinds of ordered groupoids. To understand this talk, you just need to
know what a semigroup is and how homomorphisms are represented by
congruences.
Chapter 1
These are the
detailed notes that prove all the assertions made in the lecture.
Lecture 2
Monday at 10.00.
Building
inverse
semigroups from categories (Draft).
Inverse semigroups can be described in terms of categories in at least
two ways. The first, touched on in lecture 1, is as special kinds of
ordered groupoids. In this lecture, I shall make the ordered groupoid
approach precise, and then describe a different way of
using categories to describe inverse semigroups. This originated,
unlikely as it might seem, in Girard's work in linear logic and a paper
on certain kinds of groups by Patrick Dehornoy. To understand this
talk, you just need to know the most basic category theory, and it
might
help to be aware that I always treat categories as 'monoids with many
identities'.
Chapter 2
These are the
detailed notes that prove all the assertions made in the lecture.
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