$\Sh{M}$ is the classifying topos of “local” $k$-algebras, which is to say that the data of a topos $\StrTop{\ETop}$ ringed in “local” $k$-algebras amounts to that of a geometric morphism $\ETop\to\Sh{M}$ whose inverse image functor associates to an object $X$ of $\Sh{M}$ the object $X\prn{\Str{\ETop}}$ of $\Str{\ETop}$-points of $X$. Note that to give an $\Str{\ETop}$-point $p:1\to X\prn{\Str{\ETop}}$ of $X$ amounts to giving a factorization