In mathematics, especially in differential and algebraic geometries, an inertia stack of a groupoid "X" is a stack that parametrizes automorphism groups on formula_1 and transitions between them. It is commonly denoted as formula_2 and is defined as inertia groupoids as charts. The notion often appears in particular as an inertia orbifold.
Inertia groupoid.
Let formula_3 be a groupoid. Then the inertia groupoid formula_4 is a grouoiud (= a category whose morphisms are all invertible) where
For example, if "U" is a fundamental groupoid, then formula_4 keeps track of the changes of base points.
Further reading.