How to print jquery object/array

var arrofobject = [{"id":"197","category":"Damskie"},{"id":"198","category":"M\u0119skie"}];

$.each(arrofobject, function(index, val) {
    console.log(val.category);
});

What you have from the server is a string like below:

var data = '[{"id":"197","category":"Damskie"},{"id":"198","category":"M\u0119skie"}]';

Then you can use JSON.parse function to change it to an object. Then you access the category like below:

var dataObj = JSON.parse(data);

console.log(dataObj[0].category); //will return Damskie
console.log(dataObj[1].category); //will return Męskie