Coequalizers of kernel pairs - #343
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This is a follow-up to #342 and adds the following two properties of categories:
These are closely related to existing properties in the database, such as being regular or having quotients of congruences (and their dual properties, respectively).
The properties have been decided for all categories in the database. A lemma about colimits of sequences of monomorphisms that has been removed in #303 has been brought back, and a similar version has been proven, which takes care of Sch and Metc. In particular, we now have a proof that Sch is not regular. Some proofs of regularity for subcategories (such as Grpc) have been improved by generalizing a lemma that was previously only used for LRS.
The broader context of this PR is the goal of having all constituents of a property in the database also recorded in the database. That is, if a property P is defined by "A and B and C are satisfied", we should try to add A, B, C separately and record the equivalence P ⇔ A + B + C. Deciding A, B, and C for all categories in the database then gives a more detailed understanding of P, and in many cases, multiple proofs can be combined into one (see for example the changes to Metc in this PR). The next step in this regard is, of course, to add the property that regular epimorphisms are stable under pullback. Then we will have added all the constituents of the property of being regular. EDIT. This is #344.