# Borel morphism

###### Definition 0.1.

Let ${\mathbb{G}}_{B}$ and ${\mathbb{G}}_{B}$* be two groupoids whose object spaces are Borel. An algebraic morphism from ${\mathbb{G}}_{B}$ to ${\mathbb{G}}_{B}$* is defined as a left action of ${\mathbb{G}}_{B}$ on ${\mathbb{G}}_{B}$* which commutes with the multiplication on ${\mathbb{G}}_{B}$. Such an algebraic morphism between Borel groupoids is said to be a Borel morphism if the action of ${\mathbb{G}}_{B}$ on ${\mathbb{G}}_{B}$* is Borel (viz. ref. [1])

## References

• 1 M.R. Buneci. 2006., http://www.utgjiu.ro/math/mbuneci/preprint/p0024.pdfGroupoid C*-Algebras., Surveys in Mathematics and its Applications, Volume 1: 71–98.
 Title Borel morphism Canonical name BorelMorphism Date of creation 2013-03-22 18:23:36 Last modified on 2013-03-22 18:23:36 Owner bci1 (20947) Last modified by bci1 (20947) Numerical id 12 Author bci1 (20947) Entry type Definition Classification msc 60A10 Classification msc 28A12 Classification msc 28C15 Classification msc 54H05 Classification msc 28A05 Related topic BorelSpace Related topic Groupoids Related topic CategoryOfBorelSpaces Related topic MeasurableFunctions Related topic BorelMeasure Defines algebraic morphism