categories: Limits

[Tobias Schroeder <tschroed@Mathematik.Uni-Marburg.de>]

Hi,
whenever I'm teaching basic category theory, students
ask me if there is a connection between limits in the
categorical sense and limits in the analytical sense,
e.g. the limit of a sequence of real numbers.
I've never found an answer to this question.

So I'd be very grateful for answers to one of the following:
- Can the limit of a sequence of real numbers be expressed
  as a categorical limit (of course it can if the sequence is
  monotone, but what if it is not)?
- Why have people chosen the term "limit" in category theory?
  (And, by the way, who has defined it first?)

Many thanks in advance

Tobias


--------------------------------------------------------------
Tobias Schröder
FB Mathematik und Informatik
Philipps-Universität Marburg
WWW: http://www.mathematik.uni-marburg.de/~tschroed
email: tschroed@mathematik.uni-marburg.de