It does not work with a cat. You can make that analogy with whatever you want, of course, but you cannot make that experiment with an actual cat. Decoherence prevents that. You need something as isolated from the environment as possible, and without too many relevant internal degrees of freedom. In general this is easier with smaller objects such as individual atoms.
Oh now the Schrödinger's cat story/analogy/experiment/thought experiment is a quantum interference experiment, although Schrödinger does not say anything about interference. Let's put a radioactive atom in a box made of steel, and the box we put in such place where there is a few light minutes of empty space around the box. After a minute the box will be in these states:
many states where the box knows that the atom decayed at time one second
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many states where the box knows that the atom decayed at time two seconds
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many states where the box knows that the atom has not decayed yet