Mage::Registry in Magento 2
Mage::Registry in Magento 2 is very similar to the registry of Magento 1. You can find it here: \Magento\Framework\Registry
Utilize dependency injection for adding it to the constructor. As a result, you will be able to use both $registry->register($key, $value) and $registry->registry($key) methods to store / access data.