?? "rigid" and "robust" as opposite kinds of "strong" for structures ... guaranteeing others's survival (like mine canary ...) vs surviving oneself ... under action by permutations .... ???? .... strong in breaking symmetry, vs in ... ??? getting along with it ??? .... robust structure as adaptable, flexible, springy ... opposite of rigid ... rigid = brittle ...

?? brittle ... ?? "fragile" ... "symmetry-breaking" ambiguity ... who gets "blame" / "credit", the structure or the permutation, when the latter doesn't preserve the former .... ??? .... ??? contravariance here ???? ..... ????? ....

?? strong in "breaking" other, vs in remaining "unbroken" oneself ... with perspective shift on who breaks who .... ??? .... ??? co-operation vs competition here ??? .... ?? failure as loss for both, vs [[as win for one over other] vs [as win for other over one]] ???? ..... ??????? .....


??? idea for categorification of certain flavor of "galois connection" ??? ... ?? from boolean-valued question "is f(x) = x ?" to set(?? ...)-valued question "what are the morphisms f(x) -> x ?" ..... ???? ..... ?? "galois connection" ... "idempotent monad" .... "adjunction" .... "monad" .... ???? .... ???? confusion about specialness (???? .... ?? of ... ?? particular flavor of galois connection .... ???? ....) here ??? .... ???? ....