Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with limits-and-colimits
Search options not deleted
user 75
For questions on limits and colimts in the sense of category theory, and related notions.
21
votes
Accepted
Direct limit of compact topological spaces
A $T_1$ colimit $X$ of a sequence of compact spaces $X_n$ is compact iff there is some $n$ such that the map $X_n\to X$ is surjective. This condition is obviously sufficient; suppose that it fails. …
- 31.2k
13
votes
Is there a category in which finite limits and directed colimits *don't* commute
Consider the poset of closed subsets of $[0,1]$. Let $a=\{0,1\}$ and $b(r)=[0,r]$ for $r<1$. Then the (directed) colimit of the $b(r)$ is $b=[0,1]$, and the product (i.e., intersection) of $b$ and a …
- 31.2k
9
votes
Accepted
Maximum cardinality of a filtered limit of finite sets
You can get arbitrarily large cardinalities. For instance, let $X$ be any set and consider the poset $I$ of finite partitions of $X$, ordered by refinement. There is a "tautological" filtered system …
- 31.2k