Sophie and I used to share a house with a three-legged cat named Hobbes. There were a lot of jokes about what happened to Hobbes' fourth leg ("We ate it." "It's in a reliquary at the Vatican." "We donated it to a two-legged cat"). The truth is he was hit by a car as a kitten. Didn't slow him down, happily.
Sophie learned quickly that Hobbes was not fair game for chasing, though she would lick his face in an attempt to get him to run. When he got tired of that, he would retreat to the basement where she wasn't allowed.
Then Doogie came along, and he hated cats. Sophie picked up from him that felines must be chased at all costs. After Doogie died, she had to unlearn her bad behavior with some help from the Voice of Doom. She still lunges if she sees a cat, but a sharp "Leave it!" from me pulls her up short. Friendly cats will even get a suspicious sniff (and I get an accusing look of betrayal).
Most of the time now, though, she doesn't see cats at all. As long as they don't move, she's clueless.
I hope my next poodle is as easy to teach that Kitties Are Our Friends.