Which rat or mouse is this?

Answer

This is a brown rat (Rattus norvegicus): shaggy, gray-brown fur, small, finely furred ears, and a thick, scaly tail that is shorter than the body.

Originally, the brown rat was only found in East Asia, but from the end of the Middle Ages the species has spread all over the world through human trade routes and shipping lines. The animal knows how to adapt very well to humans. But they can form pests and transmit diseases. In that sense, your cat has done a good job!