Simplest way would be to add a class with a pseudo element to the div on the click event.
CSS :
.product-to-be-categorized {
position:relative;
width:50%
}
.product-to-be-categorized img {
display:block;
width:100%;
}
.overlay:before {
content:'';
position:absolute;
width:100%;
height:100%;
background: rgba(0, 0, 0, 0.5);
}
jQuery :
$('.product-to-be-categorized').click('click', function (event) {
$(this).addClass('overlay');
});
(if you need to toggle the overlay, just replace ".addClass" by ".toggleClass" in jQuery code)