  We introduce Artin-Wraith glueing and locally closed inclusions in double
categories. Examples include locales, toposes, topological spaces, categories,
and posets. With appropriate assumptions, we show that locally closed
inclusions are exponentiable, and the exponentials are constructed via
Artin-Wraith glueing. Thus, we obtain a single theorem establishing the
exponentiability of locally closed inclusions in these five cases.
