Allowing or preventing a cat from entering the house

In slightly advanced houses that have a cat, the door which allows the cat to enter or depart the house is controlled by an electric circuit, triggered by a magnet in the cat's collar. However, in this modified circuit (details available at this link), the system checks whether the cat is carrying an animal such as a mouse. If it does this, then the cat will let loose the animal inside the house and chase it all around, dirtying the house and acting in generally a very cruel way. So, the circuit is modified to prevent the cat access if it is carrying an animal in its mouth.