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$GL_n$ is a representable functor, $GL_n(A)=Hom_{Ring}(\mathbb{Z}[x_{ij},y| 1 \leq i,j, \leq n]/(y(det(x_{ij}))-1),A)$$GL_n(A)=Hom_{Ring}(\mathbb{Z}[x_{ij},y| 1 \leq i,j \leq n]/(y \cdot det(x_{ij})-1),A)$, and thus commutes with limits.
$GL_n$ is a representable functor, $GL_n(A)=Hom_{Ring}(\mathbb{Z}[x_{ij},y| 1 \leq i,j, \leq n]/(y(det(x_{ij}))-1),A)$, and thus commutes with limits.
$GL_n$ is a representable functor, $GL_n(A)=Hom_{Ring}(\mathbb{Z}[x_{ij},y| 1 \leq i,j \leq n]/(y \cdot det(x_{ij})-1),A)$, and thus commutes with limits.
