This answer here show you how to retrieve the element by name. However, the tricky part here is that your have brackets within the name itself. So, to get around this, you need to add quotes " around the name like in the following example below.
Once you have the element, you can simple do .prop('checked')
to retrieve the current value.
$('.checkbox').click(function () {
console.log(this);
var theValue = $('input[name="gender[women]"]').prop('checked'); //<--HERE IS HOW YOU GET THE VALUE
console.log(theValue);
$.ajax({
type:'POST',
url: '/loadProducts',
data: {},
success: function(response) {
console.log(response);
$('.js-products').html(response);
}});
return false;
});