There is another related construction of root stacks with sections. Given the data above, let formula_146 be a section. Then the formula_113-th root stack of the pair formula_148 is defined as the lax 2-functorformula_149sending an formula_1-scheme formula_132 to the category whose objects line bundles of the formformula_152and morphisms are given similarly. These stacks can be constructed very explicitly, and are well understood for affine schemes. In fact, these form the affine models for root stacks with sections. Given an affine scheme formula_153, all line bundles are trivial, hence formula_154 and any section formula_155 is equivalent to taking an element formula_156. Then, the stack is given by the stack quotientformula_157withformula_158If formula_159 then this gives an infinitesimal extension of formula_160.