[Edit: Maybe I'm just completely in the wrong category. I'm finding stuff in "Ads & Affiliates" that looks like it does most of not all of this. I would never have even given that section a second glance... thinking that all... well... crap for ads and affiliates.

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I'm looking for a component that can be used to sort and order by category metric craptons of links.
This is for a public library's web page, which has hundreds of online resources and subscription databases cataloged for researcher use. They need to be able to include a description (possibly with an image or clip art in that description or beside the link.) Additionally, links need to be able to be tagged with a category or keyword. (ex. Science, Sports, Travel, Kids, etc.)
It would also need to support multiple categories per link, which is important- often links will be mentioned under multiple subject headings (ex. Biography & Science) so it would have to come up on both... however they wanted to avoid the setup they have now where a separate link appears on each page. Instead of having to remember to change every instance of that link in every category it is in whenever there is a change, they'd like to be able to have all links all in one central and easy-to-edit place that can then be called as-needed into different pages on the site by using these topic/categories.
Joomla's built-in links manager might be able to be set up close... I'm still prodding noobishly at that trying to make something usable, but I haven't figured out a search yet... it's just a bunch of menu'd links. It also doesn't appear to support multiple categories for the same link.
My search-fu is weak... and I'm not really sure what they're actually called. Anything "database" keeps finding me SQL tools, and "Links manager" are coming up all about affiliates and sharing links, not cataloging them. This sounds like something that would be common for any educational page, or managing large amounts of information... just having crap of all luck finding the right thing while looking through what's available on extensions.joomla.org.
Thank you.
-L
Apologies if this is the wrong forum, or if there is a better place for these kinds of requests. Components were the most elaborate of extensions, right? The Component/Plugin/Module thing is still a bit confusing. (Something like this would probably involve all three, wouldn't it?) I just switched to Joomla after a few years of managing DotNetNuke, where "things you stick on your page" were all just modules, and Snowcovered was my second home. <.<