请尝试以下操作：

var categories = [
    {catValue:1, catName: 'Arts, crafts, and collectibles'},
    {catValue:2, catName: 'Baby'},
    {catValue:3, catName: 'Beauty and fragrances'},
    {catValue:4, catName: 'Books and magazines'},
    {catValue:5, catName: 'Business to business'},
    {catValue:6, catName: 'Clothing, accessories, and shoes'},
    {catValue:7, catName: 'Antiques'},
    {catValue:8, catName: 'Art and craft supplies'},
    {catValue:9, catName: 'Art dealers and galleries'},
    {catValue:10, catName: 'Camera and photographic supplies'},
    {catValue:11, catName: 'Digital art'},
    {catValue:12, catName: 'Memorabilia'}
];

var categoriesJson = JSON.stringify(categories);
var mainCat = ['Arts, crafts, and collectibles', 'Baby' , 'Antiques']

$.each(JSON.parse(categoriesJson) , function (key, value) {
  if(mainCat.indexOf(value.catName) > -1){
   console.log('Exists: ' +value.catName)
 }
 else{
   console.log('Does not exists: ' +value.catName)
 }
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>

我将filter初始数据数组以获得匹配类别的数组：

var matchedCategories = categories.filter(i => mainCat.indexOf(i.catName) >= 0);

然后，您可以通过迭代这个子数组来完成您需要的操作。

我也使用 @dhilt 方法，但使用包含
例如，如果包含一个（返回bool）

categories.filter(i =>
    mainCat.includes(i.catName)
  ).length > 0
    ? true
    : false;