A strongly connected site is a site satisfying sufficient conditions to make its topos of sheaves into a strongly connected topos.
Let be a locally connected site; we say it is a strongly connected site if it is also a cosifted category
If is strongly connected site, then the sheaf topos is a strongly connected topos.
Because the left adjoint in the sheaf topos over a locally connected site is given by the colimit functor and colimits preserve finite products on the sifted category .
and
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