A scheme immersion is a morphism 
that factors as a closed
immersion 
followed by the open immersion 
of an open subscheme 
of 
. It identifies 
with a locally closed
subscheme of 
(Stacks Project 2026).
An open immersion identifies its source with an open subscheme of its target. A closed immersion identifies its source with a closed subscheme and is locally induced by a quotient ring.
Scheme immersions are distinct from immersions of smooth manifolds.
