  The concern of this paper is a famous combinatorial formula known under the
name "exponential formula". It occurs quite naturally in many contexts
(physics, mathematics, computer science). Roughly speaking, it expresses that
the exponential generating function of a whole structure is equal to the
exponential of those of connected substructures. Keeping this descriptive
statement as a guideline, we develop a general framework to handle many
different situations in which the exponential formula can be applied.
