Let be a groupoid.
A permutation representation of is a representation of on Set, i.e. a functor .
A linear permutation representation is a functor Vect that factors through a permutation representation via the free functor which sends a set to the vector space for which this set is a basis.
Notably for the delooping groupoid of a group , a permutation representation is a set equipped with a -action.
is the classifying topos for the group .
For other general perspectives on this see also at infinity-action the section Examples – Discrete group actions on sets.
Revised on October 15, 2015 12:55:10
by Todd Trimble