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This PR fixes #63 in a systematic way by introducing quotient object classifiers (the formal dual to subobject classifiers). The deduction system should be able to dualize the implications for regular subobject classifiers as well (in particular, the result that every additive category with this property is trivial), which is why regular quotient object classifiers have been added as well. They are a bit weaker and have much more chance to exist, but it turns out, they usually don't.
As usual, the new properties are decided for all categories in the database (with one exception: Ban). To to this efficiently, I have improved the implication
subobject classifier + thin => trivialtosubobject classifier + strict terminal object => trivialand also added a lemma to descend subobject classifiers to coreflective subcategories.I have noticed that some of the proofs are a bit ad hoc and that they can be improved by adding four new properties to the database, which all apply only to categories with zero morphisms: has kernels, has cokernels, is normal, is conormal. Adding them (assignments + some implications) will make some of the current proofs for missing subobject classifiers and missing quotient object classifiers redundant. This will be done in a later PR.