PlanetPhysics/Borel Morphism

Let $$\grp_B$$ and $$\grp_B$$* be two groupoids whose object spaces are Borel. An \htmladdnormallink{algebraic {http://planetphysics.us/encyclopedia/CoIntersections.html} morphism} from $$\grp_B$$ to $$\grp_B$$* is defined as a left action of $$\grp_B$$ on $$\grp_B$$* which commutes with the multiplication on $$\grp_B$$. Such an algebraic morphism between Borel groupoids is said to be a Borel morphism if the action of $$\grp_B$$ on $$\grp_B$$* is Borel (viz. ref. )