Sortd is a ‘skin’ for Gmail, implemented as a Chrome extension, and attempting to integrate task management directly into the email inbox experience, along with conventional email. The company has also developed an iOS app, which I haven’t had a chance to fool with, yet.
Here you see a screenshot (courtesy of OSM), showing four columns. The leftmost is the email inbox, which flattens out all emails into a single stream, even if you’ve set up Gmail folders.