  We consider the diffeological version of the Clifford algebra of a
(diffeological) finite-dimensional vector space; we start by commenting on the
notion of a diffeological algebra (which is the expected analogue of the usual
one) and that of a diffeological module (also an expected counterpart of the
usual notion). After considering the natural diffeology of the Clifford
algebra, and its expected properties, we turn to our main interest, which is
constructing pseudo-bundles of diffeological Clifford algebras and those of
diffeological Clifford modules, by means of the procedure called diffeological
gluing. The paper has a significant expository portion, regarding mostly
diffeological algebras and diffeological vector pseudo-bundles.
