nLab
prorepresentable functor

A functor C opSetC^{op}\to Set is prorepresentable (or pro-representable) if it is a small filtered limit of representables. In other words, it corresponds to a pro-object.

As these functors are ‘exactly’ the left exact functors, (at least with a caveat on size), that latter term can also be used, but there are some standard situations and conventions when this ‘pro-’ terminology is used.

Note

One tends to say ‘pro-object in CC’, and may use various descriptions via the (system of) representing objects in CC, but one does not usually say ‘prorepresentable functor in CC’.

References

Revised on December 5, 2011 19:25:23 by Tim Porter (95.147.237.179)