The way JavaScript works is:

- The web page points to a JavaScript program.
- Your browser transparently downloads that JavaScript program,
temporarily installing it into the browser.
- Your browser executes the JavaScript program where the web page
specifies it should.

JavaScript code gets executed on your computer, not on a remote
server.[0] So in effect, the GNU AGPL is exactly the same as the GNU GPL
for these programs.

Now, for your actual question: the various JavaScript files are
generally several different programs that just happen to be loaded by
the same web page. It's basically the same situation as having several
different programs installed in your OS: a bunch of unrelated programs
are perfectly able to coexist on the same computer, regardless of
license restrictions. For example, software under version 2 of the
Apache License can be on the same system as software under version 2 of
the GNU GPL (see Android, for example; the kernel Linux is under the
GPLv2, while much of Android's userland is under the Apache License
version 2). Similarly, if a web page uses one JavaScript program under
the AGPL, that doesn't mean that some other JavaScript program it loads
is also under the AGPL.

[0] There is such a thing as JavaScript code being server-side, but I
don't think it's very common.

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