[see also: aim, motivation]
The present paper is motivated by the desire to make the subject as accessible as possible.
It seems that the relations between these concepts emerge most clearly when the setting is quite abstract, and this (rather than a desire for mere generality) motivates our approach to the subject.
[see also: wish, want, require]
Now $F$ is the desired lifting.
So $F$ must be constant on $H$, thereby showing that $A=B$, as desired $\langle$claimed/required$\rangle$.
Here $L$ can be taken as large as desired.
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