Further thoughts on categories and their applications.
References: Toposes. Theories and Triples can be found at Michael Barr's home
page, www.math.mcgill.ca/barr/. The notes suggested by Jochen, below, are a
good starting point.
Applications: There are a lot of different types of categories
John,
How do you feel about Goldblatt's book on Topoi? I've been working
through it slooowly and like it so far, but I'm not sure whether it is
leaving important things out. In particular, if you need something to
understand the exposition, say, sheaves, then he goes back and tells you
just
Carl,
I have only skimmed parts of Goldblatt's book. It did look like it was trying
to do the hard job of giving the important concepts of topos theory, along with
the basic technical details. (it is easier to assume that the readers know
category theory and also know how to digest a book that
So, you get the representation of the unknown context of a thing by somehow
knowing that the thing is not well described without it? How do you know
what you're missing?I don't get where you propose the missing
information to come from.
Phil
-Original Message-
From: [EMAIL
Phil Henshaw wrote:
So, you get the representation of the unknown context of a thing by somehow
knowing that the thing is not well described without it? How do you know
what you're missing?I don't get where you propose the missing
information to come from.
What? I don't understand.
Phil Henshaw wrote:
You seem to suggest it is 'illformed' to have local knowledge and unanswered
contextual questions.
No, not at all. One can easily have an incomplete math representation
of some aspect of a concrete thing. But one cannot have a complete math
representation of some aspect
OK. So perhaps you might be willing to change your question to:
Given
an INcomplete math representation of a button, how would you derive a
math representation of a button hole? If you did that, then we might
be able to formulate an answer. However, although that modified
question is
All,
The Wiki that supports this discussion suffered a calamity last week and has
been moved, at least for the moment. The part of the address that used to
read,
.../wiki/... now reads .../mw/... . EVERYTHING else is the same.
To find all the pieces, go to the NoodlersIndex at
