Introduction to *-Autonomous categories, continued

**Abstract:**
Next time, I will finish proving things about sigma and tau; in
particular
that tau is left adjoint to sigma. They will be used to show that the
inclusions of the categories of weak, resp. strong, objects has a
left,
resp. right, adjoint and then use generalities on adjoints to show
that they
are equivalent categories. In future lecture(s), at least one and at
most
two, I will show that the chu category is equivalent to the category
of weak
objects, and therefore to the category of strong ones. Since the chu
category is *-autonomous, so are they. Then I will discuss examples.
One
is groups. The others are actually all examples of one rather general
situation. Let K be a spherically complete field (this was new to me,
see:
https://en.wikipedia.org/wiki/Spherically_complete_field), which
includes
all locally compact fields, then there are *-autonomous categories
starting
with the normed K-spaces. This includes the case that K is discrete.