Connection is splitting of first-order symbol sequence
A connection on is equivalent to a choice of splitting for this sequence.
A splitting of the above sequence is equivalent to a section map:
which is equivalent to a map (satisfying some additional conditions):
The right side is equivalent to , so a splitting of the sequence is equivalent to a map:
satisfying some additional conditions. Clearly, a connection is also a map of the above form, so it remains to check that the additional condition that comes from it being a splitting, is equivalent to the Leibniz rule for the connection.