Well, the PIR spec says the following about output:
Alarm Outputs Form A N.C 28Vdc 0.1 A (with 10 Ohm series protection
I think this means that the output is in the form of a (electromagnetic) relay, of "Form A", "Normally Closed". The normally closed switch has a 10 Ohm in series current protecting resistor (so that no excessive current can pass the closed relay switch).
The usual wiring is the following: Extract from the relay switch, two long wires (can be as long as 100 meters say). At the end of the two wires, one end to Rpi 3V3 (just for example), another end a 10k to Rpi ground.
Then Rpi continuous monitors that the voltage at the resistor end is High (3v3) because the relay switch is closed. If the PIR detects a cat coming in, it will change the relay switch open, now Rpi will find resistor end no current flowing, therefore voltage becomes zero (actually depends of the wiring polarity).
The relay switches on/off a DC circuit (in this case, 3V3 > 10K > ground). This DC circuit has no AC circuit noise problem if the wiring is over 100 meters long (assuming connect wire is heavy duty/thick, so voltage drop is small).
In other words, 28V DC 0.1A is the relay spec. To clarify things, for example, a cheapie 5V relay module, the relay spec is similarly 200V 6/10A, DC30V 10A (for switching high power motors, lamps). In PIR case, the relay is not passing current to turn on a fan or motor, so only 28V 0.1A is enough to make a signal switch.
And of course you don't need to use Rpi. Instead you can use a status LED/buzzer which is on when no cat comes, and off otherwise.