# 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. ^{[1]})

## All SourcesEdit

^{[1]}

## ReferencesEdit

- ↑
^{1.0}^{1.1}M.R. Buneci. 2006., Groupoid C*-Algebras.,*Surveys in Mathematics and its Applications*, Volume 1: 71--98.