[[!redirects newpage subtopos]] +-- {: .num_lemma} ###### Theorem ([[nLab:Elephant]] A.4.3.9, p.192) Let $(l\dashv i):L\stackrel{i}{\hookrightarrow}E$ be a reflective subcategory of a topos such that the monad $i\circ l$ is [[nLab:cartesian monad|cartesian]] (i.e. $i\circ l$ preserves pullbacks). Then $L$ is a topos and $l$ preserves finite limits (i.e. $(l\dashv i)$ is a geometric morphism). =--