I would suggest that a motion activated water spraying cat deterrent is one of two good devices to deter a cat from coming onto your backyard and pooping. The other would be a very similar device but rather than emitting water it emits a high-pitched sound which is very hard for a person to hear but which is very audible to a domestic cat because they have ears that are particularly sensitive to high frequencies. Please click on the link above a photograph for more on this topic.
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