Inspired by Reaching kedusha during silent shemone esre among many others, and the comment, "'fulfill the obligation of someone who missed the Kedusha during the Amidah' What obligation is this exactly?" by DoubleAA, here.
Why exactly do we stop and join in with the Kedusha? We have already (presumably) said the bracha of "ata kadosh" in our silent amida, and, strictly speaking, originally, the need for any chazara was instituted only to account for those who would not daven on their own so in a case where all could daven, there would have been no "Kedusha" to say.
This question arises when I am davening with one minyan within earshot of another minyan (which happens at the Kotel among other places). If I am in the middle of my silent amidah and another minyan is saying kedusha, do I have some transcending obligation to stop (as per the requirement discussed in the linked question above) because kedusha is its own obligation or is kedusha related to the repetition of prayer which I am saying as the chazara would supplement my prayer in my minyan, so I would not be exempted of some local obligation by the kedusha from another minyan.