With writing you can cancel a city action of another player. Do I have to do that directly after his action or am I allowed to react later in my city action time or in the city action time of another player? In this case I would interpret the city action as a phase in which all players can do city actions like this at any time.
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From the Rules (page 12):
Players take city actions in turn order and take city actions one at a time. To cancel a player's city action, you have to declare that your use of the writing ability immediately after they take that city action. The cancellation has to be declared before anyone else takes a subsequent action because the cancellation could affect their later actions. So, for example, if you cancel a player building a wonder with one of their cities, they could still build it with the other. It is standard procedure in board games for you to be able to request they wait after taking an action (before taking any subsequent action) for you to decide whether or not you want to cancel it.
The game rules are ambiguous as to whether or not any trade spent to rush production is lost or not when writing is used, but this is answered in the FAQ:
With writing, you can deploy a diplomat to cancel another player's city action (at least that's the mechanic in the computer version). The diplomat can be deployed at any time on one of your turns, and will operate on an opposing city action that is underway on that turn.