s is illustrated by
the theory order <span style="font-weight: bold; font-style: italic;">T&#780;</span><small><sub>1</sub></small>
&#8805; <span style="font-weight: bold; font-style: italic;">T&#780;</span><small><sub>2</sub></small>
in the
pea-green colored small rectangle. The restriction of a fiber to the
sub-context of closed
theories corresponds precisely to the lattice of theories over the
indexing type language. Sums in the context of theories correspond to
meets in the lattices of theories (fibers)