Magento 2: Product Repositories, Filter Groups, and `AND`

Actual annotation of \Magento\Framework\Api\Search\FilterGroup says (class phpDoc):

Groups two or more filters together using a logical OR

It means that you need to create two groups with one filter in each.

In Magento 2 all the filters in same FilterGroup will be added using OR operator. But all the FilterGroup will be added using AND operator. So you will need to add multiple FilterGroups as below:

$objectManager = \Magento\Framework\App\ObjectManager::getInstance();
$searchCriteria = $objectManager->create('\Magento\Framework\Api\SearchCriteria');
$filter = $objectManager->create('\Magento\Framework\Api\Filter');
$filter->setField('category_id');
$filter->setValue(array(1, 2, 3));
$filter->setConditionType('in');

$filterGroup = $objectManager->create('\Magento\Framework\Api\Search\FilterGroup');
$filterGroup->setFilters([$filter]);

$filterEnabled = $objectManager->create('\Magento\Framework\Api\Filter');
$filterEnabled->setField('status');
$filterEnabled->setValue(\Magento\Catalog\Model\Product\Attribute\Source\Status::STATUS_ENABLED);
$filterEnabled->setConditionType('eq');

$filterGroupEnabled = $objectManager->create('\Magento\Framework\Api\Search\FilterGroup');
$filterGroupEnabled->setFilters([$filterEnabled]);


$searchCriteria->setFilterGroups([$filterGroup, $filterGroupEnabled]);

In further details and logical combinations about search criteria, you can find at Magento-2 Search Criteria