groupoid principal bundle
Classes of bundles
Examples and Applications
Special and general types
For a groupoid object a -principal bunde is a morphism with an principal action of on .
For a group object in some (∞,1)-topos (for instance ∞LieGrpd for smooth Lie groupoid-bundles), and the corresponding delooping object, -principal bundles are the (∞,1)-pullbacks of the form
One equivalently (with non-negligible but conventional chance of confusion of terminology) calls such a -groupoid principal bundle.
So more generally, for any groupoid object with collection of objects, the -pullbacks
are groupoid principal bundles .
For = and a Lie groupoid, a -prinipal bundle is locally of the form
for the source fiber over an object .
- Ieke Moerdijk, J. Mrčun, Introduction to foliations and Lie groupoids Bulletin (New Series) of the AMS, Volume 42, Number 1, Pages 105–111
Revised on April 2, 2013 21:37:59
by Urs Schreiber