Inertia stack
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In mathematics, especially in differential and algebraic geometries, an inertia stack of a groupoid X is a stack that parametrizes automorphism groups on X and transitions between them. It is commonly denoted as \Lambda X and is defined as inertia groupoids as charts. The notion often appears in particular as an inertia orbifold.
In mathematics, especially in differential and algebraic geometries, an inertia stack of a groupoid X is a stack that parametrizes automorphism groups on X and transitions between them. It is commonly denoted as \Lambda X and is defined as inertia groupoids as charts. The notion often appears in particular as an inertia orbifold. Let U = (U_1 \rightrightarrows U_0) be a groupoid. Then the inertia groupoid \Lambda U is a groupoid (= a category whose morphisms are all invertible) where the objects are the automorphism groups: \operatorname{Aut}(x), x \in U_0, the morphisms from x to y are conjugations by invertible morphisms f : x \to y ; that is, an automorphism g : x \to x is sent to f \circ g \circ f^{-1} : y \to y, the composition is that of morphisms in U . For example, if U is a fundamental groupoid, then \Lambda U keeps track of the changes of base points. ==Notes== http://pantodon.jp/index.rb?body=inertia_groupoid in Japanese
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