How to add style in functions.php depending on conditions?

So on your category page check the body tag in your developer tools. There should be a category class. You can then target that page in your CSS with that classname. This is standard CSS stuff.

.cat-name{ color: blue; }

All other pages will not have that classname and the color: rule be your default.

Answering your direct question on how to conditionally load a stylesheet:

if(is_category('cats')){ 
    wp_enqueue_style( 'stylesheet-name', get_template_directory_uri() .'/mycss/category1.css', array(), '1.1', 'all');
}

Remember categories and taxonomies can get pretty complex. Custom taxonomies and categories may not work with something as simple as is_category