closed immersion of schemes

A homomorphism $f:X\to Y$ of schemes is a **closed immersion** if it induces a homeomorphism of the underlying topological spaces (in the Zariski topology) and the comorphism $f^\sharp:\mathcal{O}_Y\to f_*\mathcal{O}_X$ is an epimorphism of sheaves on $Y$.

More generally, let us consider some category of spaces, i.e. sheaves of sets on $C = Aff$ equipped with a subcanonical Grothendieck topology. Then a morphism $F\to G$ of spaces is said to be **closed immersion** if it is representable by a strict monomorphism.

Discussion in the context of higher geometry/higher algebra is in

Last revised on November 26, 2013 at 23:43:27. See the history of this page for a list of all contributions to it.