<column name="category" class="ChillyProductsgridUiComponentListingColumnCategory">
    <argument name="data" xsi:type="array">
        <item name="options" xsi:type="object">ChillyProductsgridModelCategoryCategorylist</item>
        <item name="config" xsi:type="array">
            <item name="filter" xsi:type="string">select</item>
            <item name="dataType" xsi:type="string">text</item>
            <item name="label" xsi:type="string" translate="true">Categories</item>
            <item name="sortOrder" xsi:type="number">50</item>
        </item>
    </argument>
</column>

$fieldName = $this->getData('name');
if (isset($dataSource['data']['items'])) {
    //$categories=array();
    foreach ($dataSource['data']['items'] as & $item) {
        $p_id=$item['entity_id'];
        $product=$this->_productloader->create()->load($p_id);
        $cats = $product->getCategoryIds();
        $objectManager   = MagentoFrameworkAppObjectManager::getInstance();
        $categories=array();
        if(count($cats) ){
            foreach($cats as $cat){
                $category = $objectManager->create('MagentoCatalogModelCategory')->load($cat);
                $categories[]=$category->getName();
            }

}
$item[$fieldName]=implode(',',$categories);
    }
}
return $dataSource;

<item name="filter" xsi:type="string">select</item>

<item name="options" xsi:type="object">ChillyProductsgridModelCategoryCategorylist</item>

<filters name="listing_filters">
        <argument name="data" xsi:type="array">
            <item name="config" xsi:type="array">
                <item name="templates" xsi:type="array">
                    <item name="filters" xsi:type="array">
                        <item name="select" xsi:type="array">
                            <item name="component" xsi:type="string">Magento_Ui/js/form/element/ui-select</item>
                            <item name="template" xsi:type="string">ui/grid/filters/elements/ui-select</item>
                        </item>
                    </item>
                </item>
            </item>
        </argument>
</filters>