あがる => ...up (Upwards) N4
Direction
~むきがある(~向きがある)     => There is a tendency N1
あがる => so... (Extreme level) N4
Extreme level
ふしがある => Seem N2
Speculation
あがる => has finished doing something N4
Completed
ことがある/こともある => there are times when N5
ではあるが => Although it is N2
Evaluate
必要がある => Need/Need to N4
がある => There is; is (non-living things) N5
~には~の~がある      => has its own~ N3
Characteristic
限りがある/ない => is limited, has boundary N2
Limit, limit
甲斐がある => It’s worth one’s efforts to do something N2