  We investigate the properties of the Kleisli category KlT of a monad
(T,{\lambda},{\mu}) on a category E and in particular the existence of (some
kind of) pullbacks. This culminates when the monad is cartesian. In this case,
we show that any T-category in E in the sense of A. Burroni coincides with a
special kind of internal category in KlT . So, it is the case in particular for
T -operads and T -multicategories. More unexpectedly, this, in turn, sheds new
lights on internal categories and n-categories.
