Publish and register in CategoryModule
init
method - this will make available your css and js in category module.
Something like this:
public function init() {
$path = $this->assetManager->publish(Yii::getPathOfAlias('application.modules.category.assets'));
$this->clientScript->registerCssFile($path . '/css/some-css.css', 'screen, projection');
$this->clientScript->registerScriptFile($path . '/js/some-js.js');
}