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Fix result on regular extensive categories - #419
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There is an implication in the database saying that an extensive, regular, and epi-regular category is co-Malvev and has effective cocongruences. However, this is (probably) not correct, since it was not shown that the category is finitely cocomplete, which is part of the definition of being co-Malcev. We need to add the assumption "finitely cocomplete" (or relax the definition of co-Malvev, but this is a whole other topic), and this has been done here.
This brings several changes.
The category
Quiv_fcof quivers with finite components has an undecided property: if it is regular. Indeed, it is regular, the proof has been added, whereas before it was incorrectly deduced that it is not regular.For this reason, the two combinations
which were only witnessed by
Quiv_fc(or its dual) before, have no witness anymore. They appear in the list of missing combinations now.With the fix, we get new potentially consistent combinations. They appear in the list of missing combinations now.
Indeed, I asked Claude and it quickly came up with a pretopos that does not have coequalizers.
As a result, the number of missing combinations grows from 249 to 259.
FYI @dschepler