You say library so I wonder if you are trying to make some form of homebrew.
If not then some of the browsers support things.
There are FTP options for things, though most go for servers here (there are some clients but not great ones) so there is that. https://gamebrew.org/wiki/List_of_DS_homebrew_applications lists a bunch. Some forms of DS to DS transfer as well.
DS linux should feature a copy of wget. Don't think it got ported out to standalone like fsck did (see dsfsck)
I don't know what abilities the various forms of lua that the DS has got as far as wifi access but you could probably cobble together something reasonably easily if it does (whether you can directly run something like https://github.com/ArchiveTeam/wget-lua , want something simpler or will need to do some work I don't know).
devkitPro has an example that works for HTTP using WEP/Open security Wi-Fi networks, however it can't make use of the DSi's WPA security support or download from HTTPS sources unfortunately.
Edit: ftpd is probably the most modern libnds/devkitARM homebrew that makes use of Wi-Fi, I think it can get better speed from DSi Wi-Fi, but not the WPA security.
There's also nocash's wifiboot which is the only homebrew that can use WPA security, it's written in assembly, and nocash's special version of it at that, though so it's not super easy to copy.
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