PlanetPhysics/Borel Morphism

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