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# 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., Groupoid C*-Algebras., Surveys in Mathematics and its Applications, Volume 1: 71–98.

Defines:

algebraic morphism

Keywords:

Borel morphism, Borel groupoids, left action of a groupoid on another

Related:

BorelSpace,Groupoids,CategoryOfBorelSpaces, MeasurableFunctions, BorelMeasure

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

60A10*no label found*28A12

*no label found*28C15

*no label found*54H05

*no label found*28A05

*no label found*

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