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I expanded at cohesive site the example “Families of sets”.
I also started expanding the Examples-section at cohesive topos, but it remains stubby for the moment. I have to run now.
Mike,
at cohesive site the first axiom was “has finite products”. That was originally due to me. You had observed that more generally all we need is “cosifted”.
I have changed the axioms now to
has a terminal object
is a locally connected site;
every object has a global point
it is cosifted.
I have further expanded and polished the Examples-sections a cohesive topos and cohesve site
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