nLab
prorepresentable functor

A functor CSetC\to Set is prorepresentable (or pro-representable) if it is a small filtered colimit 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

including

For some applications see

  • Alexander I. Efimov, Valery Lunts?, Dmitri O. Orlov, Deformation theory of objects in homotopy and derived categories II: Pro-representability of the deformation functor, doi

Revised on October 26, 2015 15:52:52 by Tim Porter (2.26.19.217)