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Non-Elementary Realm-Like Structures

No. Variant 1 Variant 2 Variant 3 Variant 4
01 Monoid with given unit ... with axiom/theorem stating unique existence of unit
02 Order relation with \geq ... with < and =
03 Group with multiplication ... with division
04 Category with objects and arrows ... with arrows (and without objects)
05 Topological space with open sets ... with closed sets ... with interior operator ...
06 Untyped lambda calculus Combinatory logic