Spahn subtopos (Rev #1, changes)

Theorem (Elephant A.3.4.9, p.192)

Let $L\stackrel{i}{\hookrightarrow}E$ be a reflective subcategory of a topos such that the reflector $l$ is cartesian.

Then $L$ is a topos and $l$ preserves finite limits (i.e. $(l\dashv i)$ is a geometric morphism).