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The categories of life was a system used to classify people on Earth when, after Miracle Day, people stopped dying. Badly injured people, Categories 1 and 2, were taken to overflow camps. Those in Category 1 were secretly taken to modules and burned alive. This seemed the only way humans could die after the Miracle occurred.
In theory, the category system was necessary because the global situation was thought of as an epidemic in which victims' bodies would be burned en masse. The bodies of Category 1 individuals, potentially infectious, would otherwise remain eternally alive but legally dead under the new laws.
Even after the Modules became common knowledge, they were still used out of a lack of alternatives. Governments gave law enforcement special powers to search premises without a warrant if there was suspicion of an unlicenced Category 1 located there.
In reality, the line between the categories was dubious. A Category 1 could become Category 2, should they recover; Rex Matheson should have been killed when he was impaled by a rebar, but healed over time. Likewise, a Category 2 could slide into Category 1 without proper treatment. Individuals such as Geraint Cooper (who lapsed into a deep coma after suffering a stroke) were lumped into Category 1 with the truly brain-dead.
Slang developed for the concept, with some people referring to Category 1s as "Cat 1s." (TV: The Middle Men) Also, as death no longer existed on Earth, some replaced the verb "to kill" with "to Category 1". (TV: The Blood Line)
Those people designated Category 1 were brain dead or otherwise unable to function. In the overflow camps, Category 1 patients were designated with a red clothes peg and sent to the modules to be burned. (TV: The Categories of Life)
Category 2s were those with non-fatal but permanent injuries. Though Category 2s might be severely injured, they were not brain dead and could function with a degree of independence. In the overflow camps, Category 2 patients were identified with a blue peg. (TV: The Categories of Life)
Category 0 was a proposed category that would consist of anyone, of any category, deemed fit for the modules for moral reasons, such as criminals who would have received the death penalty prior to the Miracle. (TV: End of the Road) Rex Matheson unwittingly predicted this category after learning of the categories. He believed that after starting with the Category 1s, it would move onto convicted felons and illegal immigrants, "hell, anyone we don't like." (TV: The Middle Men) Oswald Danes later learned from Jilly Kitzinger that he had been classified as Category 0, after which he went underground; Jilly implied that the category had been specifically created with Oswald in mind. (TV: End of the Road)
At least two people did not fall into any of the categories. Jack Harkness was mortal, (TV: Rendition, et al) and Angelo Colasanto was in a null field, so was therefore not affected by the Miracle and mortal too. (TV: End of the Road)