Is promptly a synonym of quickly?

Yes, "promptly" is often a synonym of "quickly," though it carries a slightly different connotation.

Quickly emphasizes the speed of the action, while promptly emphasizes the timeliness or punctuality of the action.

Here's an example:

* Quickly: "The cat ran quickly across the street." (Focus is on the speed of the cat's movement)

* Promptly: "She responded promptly to my email." (Focus is on the timeliness of her response)

However, "promptly" can also sometimes imply a sense of speed, especially when referring to actions that should be done without delay.

So, while "quickly" and "promptly" aren't completely interchangeable, they can often be used synonymously depending on the context.