(I think there's a typo in the first snake equation, John – surely it should be cup of \\(X^\text{op}\\) not cup of \\(X\\))

(Also in the second one, shouldn't the arrows in the left hand diagram go the other way? otherwise it's just the first one, but "op".)

(Also in the second one, shouldn't the arrows in the left hand diagram go the other way? otherwise it's just the first one, but "op".)