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The issue with your code is as follows:
document.getElementById("SetCategory").classList.add({{ $category->name }}' ')
This snippet is not valid in JavaScript and does not adhere to correct C syntax.
Here are a couple of steps to troubleshoot:
1) Familiarize yourself with using the web browser's inspector tool (Console Tab) in Chrome, Firefox, Edge, and IE 11 by pressing F12. This will display an error message like
Uncaught SyntaxError: Unexpected token {
in the console output.
2) For JavaScript documentation, the MDN web docs are a valuable resource. You can refer to the classList section here: https://developer.mozilla.org/en-US/docs/Web/API/Element/classList. Specifically, check out line 9 of the first code example on that page, which looks like this:
const div = document.createElement('div');
div.className = 'foo';
// Initial state: <div class="foo"></div>
console.log(div.outerHTML);
// Using the classList API to manipulate classes
div.classList.remove("foo");
div.classList.add("anotherclass");
// Result: <div class="anotherclass"></div>
console.log(div.outerHTML);