groupoid action

Definition 0.1.

Let 𝒢 be a groupoidPlanetmathPlanetmathPlanetmath and X a topological spaceMathworldPlanetmath. A groupoid action, or 𝒢-action, on X is given by two maps: the anchor map π:XG0 and a map μ:X×G0G1X, with the latter being defined on pairs (x,g) such that π(x)=t(g), written as μ(x,g)=xg. The two maps are subject to the following conditions:

  • π(xg)=s(g),

  • xu(π(x))=x, and

  • (xg)h=x(gh), whenever the operations are defined.

Note: The groupoid action generalizes the concept of group action in a non-trivial way.

Title groupoid action
Canonical name GroupoidAction
Date of creation 2013-03-22 19:19:23
Last modified on 2013-03-22 19:19:23
Owner bci1 (20947)
Last modified by bci1 (20947)
Numerical id 9
Author bci1 (20947)
Entry type Definition
Classification msc 22A22
Classification msc 18B40
Synonym action
Related topic GroupAction
Related topic Groupoid
Related topic GroupoidRepresentation4
Defines anchor map