Lemma 61.3.7. Let $p : (Y, \mathcal{O}_ Y) \to (X, \mathcal{O}_ X)$ and $q : (Z, \mathcal{O}_ Z) \to (X, \mathcal{O}_ X)$ be morphisms of locally ringed spaces. If $\mathcal{O}_ Y = p^{-1}\mathcal{O}_ X$, then

is bijective. Here $\text{LRS}/(X, \mathcal{O}_ X)$ is the category of locally ringed spaces over $X$ and $\textit{Top}/X$ is the category of topological spaces over $X$.

## Comments (2)

Comment #820 by Pieter Belmans on

Comment #821 by Johan on