I came across the notion of inductive limits in C*-algebras, where they exist. Except for the category of finite sets, what are natural examples of categories which fail to have inductive limits?
Categories without inductive limits
1
$\begingroup$
functional-analysis
category-theory
-
0I guess examples like "a non-complete boolean algebra considered as a category" don't count for you either? Obviously, categories with all (co)limits are nice, and one tries to avoid studying categories which are not nice. – 2012-03-16
-
2Since your question is tagged functional analysis: The categories of Banach/Fréchet/Hilbert spaces with bounded linear maps or separable $C^\ast$-algebras or general Banach algebras would be natural examples. – 2012-03-16
-
0@Zhen: from an analytic perspective completeness is often a bit too much to ask for and I insist that the categories I mentioned are nice and natural. :) – 2012-03-16
-
1The category of fields doesn't have coproducts, much less arbitrary direct limits. – 2012-03-16
-
0Thank you for your comments. – 2012-03-17