Stable general linear group
= Stable general linear group
{title2=$\mathrm{GL}_\infty(A)=\varinjlim_n\mathrm{GL}_n(A)$}
The union of finite invertible <matrices> under $g\mapsto\operatorname{diag}(g,1)$. Every element and relation occurs in a finite <matrix> size; adding identity blocks permits comparisons between different sizes without changing the stable class.