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By a sketch we here mean a small category 5 together with a small set $ of protective cones in S , each cone ( J > € $ being indexed by a small category L, . A model of S in any category 8 is a functor G : S -*• 8 such that each G is a limit-cone. Let F be any small set of small categories containing all the L, . A small category T admitting all F-limits (that is, an F-complete small T ) is called an F-theory; it is considered as a sketch in which the distinguished cones are all thedoi:10.1017/s0004972700005591 fatcat:uyorzltt35ed3k27oitjoqn7ei