Dave Lister, a 3rd Technician on board the Red Dwarf, a mining ship, gets in trouble for smuggling a cat aboard ship.  He opts to go into time stasis rather that submit his cat to death.  When he awakens, he finds that he's the only one left alive and that 3 million years have passed.  A holographic Rimmer, his ex bunk-mate is all that left to keep him company - and the evolved descendants of his cat.