§ Splitting of semidirect products in terms of projections
Say we have an exact sequence that splits:
with the section given by such that .
Then we can consider the map . See that this firsts
projects down to , and then re-embeds the value in . The cool thing is that
this is in fact idempotent (so it's a projection!) Compute:
So this "projects onto the value". We can then extract out the component as