Many of the components or structures from which a nuclear reactor is made are made of metal. Cobalt occurs naturally in ores along with other metals such as nickel and iron. When these metal parts are exposed to the neutron radiation, generated when the uranium atoms split, the cobalt undergoes transmutation, the fancy name for when one element changes into another by radioactive decay, nuclear bombardment, or similar processes.
So, as far as I know, cobalt is not intentionally used in nuclear reactors. Rather it is a by-product of the reactivity that occurs from the uranium atom splitting or fission that takes place in the core of the nuclear reactor.
D. United States, China, United Kingdom, France, Russia, India, Pakistan, Israel, North Korea