It's strange to have Ardour and Reaper up there with ProTools and Logic described as a MIDI sequencer. That's how it started but at some point it crossed over into a full-featured professional DAW and I'm not sure even Reaper has caught up to its live instrument mixing and editing capabilities.
Ableton is literally a sequencer (and much more) and probably belongs in your MIDI sequencer category.
Ableton is literally a sequencer (and much more) and probably belongs in your MIDI sequencer category.