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It is known that the natural functor of smooth functions from the category of smooth manifolds into the category of locally ringed spaces is a full embedding (see, for example, here). Is a similar ...

Let $X$ be a locally ringed space. We have for a point $p$ the exact sequence $$0\to \mathfrak{m}_p^2\to \mathfrak{m}_p\to \mathfrak{m}_p/\mathfrak{m}_p^2 \to 0$$ where $\mathfrak{m}_p$ is the maximal ...