The example about stacks in 1.2 has a certain irony in context. This requires a small mathematical parenthese:
A stack is a certain sophisticated type of geometric structure which is increasingly used in algebraic geometry, algebraic topology (and spreading to some corners of differential geometry) to make sense of geometric intuitions and notions on “spaces” which occur “naturally” but are squarely out of the traditional geometric categories (like manifolds, schemes, etc.).
The upshot of this vague outlook is that in the relevant fields, everything of interest is a stack (or a more exotic beast like a derived stack), precisely because the notion has been designed to be as general and flexible as possible ! So asking someone working on stacks a good example of something which is not a stack is bound to create a short moment of confusion.
Even if you do not care for stacks (and I wouldn’t hold it against you), if you are interested in open source/Internet-based scientific projects, it is worth having a look at the web page of the Stacks project (http://stacks.math.columbia.edu/), a collaborative fully hyperlinked textbook on the topic, which is steadily growing towards the 3500 pages mark.
The example about stacks in 1.2 has a certain irony in context. This requires a small mathematical parenthese:
A stack is a certain sophisticated type of geometric structure which is increasingly used in algebraic geometry, algebraic topology (and spreading to some corners of differential geometry) to make sense of geometric intuitions and notions on “spaces” which occur “naturally” but are squarely out of the traditional geometric categories (like manifolds, schemes, etc.).
See www.ams.org/notices/200304/what-is.pdf for a very short introduction focusing on the basic example of the moduli of elliptic curves.
The upshot of this vague outlook is that in the relevant fields, everything of interest is a stack (or a more exotic beast like a derived stack), precisely because the notion has been designed to be as general and flexible as possible ! So asking someone working on stacks a good example of something which is not a stack is bound to create a short moment of confusion.
Even if you do not care for stacks (and I wouldn’t hold it against you), if you are interested in open source/Internet-based scientific projects, it is worth having a look at the web page of the Stacks project (http://stacks.math.columbia.edu/), a collaborative fully hyperlinked textbook on the topic, which is steadily growing towards the 3500 pages mark.