Definition 0.1
Let

and

* be two
groupoids
whose object spaces are Borel. An
algebraic morphism from

to

* is defined as a left action of

on

* which commutes with the multiplication on

. Such an algebraic morphism between
Borel groupoids
is said to be a
Borel morphism if the action of

on

* is Borel (viz. ref. [
1])