Pullbacks imply coreflexive equalizers

[ScriptRaccoon]

Any category with pullbacks has coreflexive equalizers. Dually, any category with pushouts has reflexive coequalizers. This result was missing and has now been added. Unfortunately, no property assignments have become redundant after adding this. But: the number of consistent combinations without witnesses has decreased from 481 to 467, which contributes to this milestone. This is because the following 14 combinations have become inconsistent, so that they do not require any witnesses anymore.

locally cartesian closed ∧ ¬coquotients of cocongruences
locally cartesian closed ∧ ¬coreflexive equalizers
locally cocartesian coclosed ∧ ¬quotients of congruences
locally cocartesian coclosed ∧ ¬reflexive coequalizers
locally poly-presentable ∧ ¬coquotients of cocongruences
locally poly-presentable ∧ ¬coreflexive equalizers
pullbacks ∧ ¬coquotients of cocongruences
pullbacks ∧ ¬coreflexive equalizers
pushouts ∧ ¬quotients of congruences
pushouts ∧ ¬reflexive coequalizers
wide pullbacks ∧ ¬coquotients of cocongruences
wide pullbacks ∧ ¬coreflexive equalizers
wide pushouts ∧ ¬quotients of congruences
wide pushouts ∧ ¬reflexive coequalizers