Definition 0.1
If

is a
groupoid
(for example, considered as a
category
with all
morphisms
invertible)
then we can construct an
-algebroid,

as follows. The
object
set of

is the same as that of

and

is the free

-module on the
set

, with
composition
given by the usual bilinear rule, extending the
composition of

.
Definition 0.2
Alternatively, one can define

to be the set of
functions

with finite support, and then we define the
convolution
product as follows: