obesessions with mutible detachments

so let's say I have a petrol detachment with the only Kabal and another one with only wych cult, could I give both an obsession?

a little confused with this, thanks

As long as each detachment (in this case patrols) contains only units from the same sub-faction (wych cult, kabal, haemonculus coven) or mercenaries (scourge, incubi, mandrakes) then each detachment can choose an obsession

So your kabal patrol could have the poison tongue obsession and your wych cult patrol could be cult of the red grief obsession as long as the above post is true

The above post is true.

Obsessions work on a per-Detachment basis.