The Stacks project

85.19 Monomorphisms

Here is the definition.

Definition 85.19.1. Let $S$ be a scheme. A morphism of formal algebraic spaces over $S$ is called a monomorphism if it is an injective map of sheaves.

An example is the following. Let $X$ be an algebraic space and let $T \subset |X|$ be a closed subset. Then the morphism $X_{/T} \to X$ from the formal completion of $X$ along $T$ to $X$ is a monomorphism. In particular, monomorphisms of formal algebraic spaces are in general not representable.

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