Spahn subtopos

Theorem (Elephant A.4.3.9, p.192)

Let (li):LiE(l\dashv i):L\stackrel{i}{\hookrightarrow}E be a reflective subcategory of a topos such that the monad ili\circ l is cartesian (i.e. ili\circ l preserves pullbacks).

Then LL is a topos and ll preserves finite limits (i.e. (li)(l\dashv i) is a geometric morphism).

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