I've the next Nav:

<li id="categories">
    <ul>
        <li class="cat-item cat-item-8 current-cat"><a href="#">Link</a>
            <ul>
                <li class="cat-item"><a href="#">Link</a></li>
                <li class="cat-item"><a href="#">Link</a></li>
                <li class="cat-item"><a href="#">Link</a></li>
                <li class="cat-item"><a href="#">Link</a></li>
            </ul>
        </li>
        <li class="cat-item cat-item-10"><a href="#">Link</a>
            <ul>
                <li class="cat-item"><a href="#">Link</a></li>
                <li class="cat-item"><a href="#">Link</a></li>
                <li class="cat-item"><a href="#">Link</a></li>
                <li class="cat-item"><a href="#">Link</a>
                    <ul>
                        <li class="cat-item"><a href="#">Link</a></li>
                        <li class="cat-item"><a href="#">Link</a></li>
                        <li class="cat-item"><a href="#">Link</a></li>
                        <li class="cat-item"><a href="#">Link</a></li>
                    </ul>
                </li>
            </ul>
        </li>
    </ul>
</li>

and also the following JS:

jQuery("#categories li.cat-item").each(function(){
    var item = jQuery("<span>").addClass('plus'),
        that = jQuery(this);

    if ( that.has("ul").length ) {   
        item.click(function(e){
            var self = jQuery(this);
            self.text( self.text() === "+" ? "-" : "+" )
                .parent().next().toggle();
            e.preventDefault();
        }).text('+');

        that.find(".children").hide();
    }

    that.children("a").prepend( item );
});

This develops a pleasant toggle menu for my groups.

However things i would like it to do is dependant on what category I'm presently viewing show the related menu to become opened up once the user arrives at the page. This needs to dedicate yourself both posts and groups.

Thanks.

Have Wordpress place the course title into an ID on the parent container (the BODY tag) after which write the CSS for every category/ID pair that opens the related menu.

Just put this after your code:

jQuery('#categories .current-cat span.plus:first').click();

which models a click the first plus sign in the present category.

If you wish to possess the whole tree to become broadened, just omit the :first:

jQuery('#categories .current-cat span.plus').click();

Btw recption menus didn't collapse when i attempted it, I needed to improve your code to that.children("ul").hide();

Update:

If .current-cat is on the li aspect in a subtree, this can be done:

jQuery('#categories .current-cat').parents('li:not(#categories)')
                                  .andSelf()
                                  .find('span.plus:first').click();

This finds all parents li, includes the present li (andSelf(), just in case it's the again a cause of a subtree) and clicks the very first + register all these.