A direct limit is the same thing as a colimit, which was often used before the categorical terminology started to become ‘standardised’. It is still used in certain areas of mathematics. (Similarly, an inverse limit is the same thing as a limit.) In this context, a direct system is the same thing as a diagram, and a direct cone is the same thing as a cocone.

Many authors restrict this terminology to limits over directed sets (or filtered categories); see directed colimit (or filtered colimit) for discussion of this case if you think that it may be what you want, or see colimit for the more general notion. Especially common is the directed set $(\mathbb{N},\leq)$ of natural numbers, in which case the direct system may be called a direct sequence.

Last revised on April 27, 2012 at 16:03:00.
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