Page "Connection (principal bundle)" Paragraph 13

The bundle TP / G is called the bundle of principal connections.

A section Γ of dπ: TP / G → TM such that Γ: TM → TP / G is a linear morphism of vector bundles over M, can be identified with a principal connection in P. Conversely, a principal connection as defined above gives rise to such a section Γ of TP / G.