Another class of gerbes can be found using the construction of root stacks. Informally, the formula_113-th root stack of a line bundle formula_124 over a scheme is a space representing the formula_113-th root of formula_54 and is denoted<math>\sqrtname=":0"></ref>pg 52 The formula_113-th root stack of formula_54 has the propertyformula_129as gerbes. It is constructed as the stackformula_130sending an formula_1-scheme formula_132 to the category whose objects line bundles of the formformula_133and morphisms are commutative diagrams compatible with the isomorphisms formula_134. This gerbe is banded by the algebraic group of roots of unity formula_135, where on a cover formula_132 it acts on a point formula_137 by cyclically permuting the factors of formula_72 in formula_139. Geometrically, these stacks are formed as the fiber product of stacksformula_140where the vertical map of formula_141 comes from the Kummer sequenceformula_142This is because formula_143 is the moduli space of line bundles, so the line bundle formula_124 corresponds to an object of the category formula_145 (considered as a point of the moduli space).