In this note we give a definition of stable maps into the classifying stack $\BGL_r$ of the general linear group. To support our belief that the definition is the correct one, we show that there are natural boundary morphisms between the moduli groupoids parameterizing stable maps to $\BGL_r$.
Representations of surface groups in the general linear group
A Modular Compactification of the General Linear Group
The field of moduli and fields of definition of dessins d'enfants
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