  We extend some fundamental definitions and constructions in the established
generalisation of Lie theory involving Lie groupoids by reformulating them in
terms of groupoids internal to a well-adapted model of synthetic differential
geometry. In particular we define internal counterparts of the definitions of
source path and source simply connected groupoid and the integration of
$A$-paths. The main results of this paper show that if a classical Hausdorff
Lie groupoid satisfies one of the classical connectedness conditions it also
satisfies its internal counterpart.

Category Theory