Definition. Cocontinuous endofunctors on \textbf {Cpo}^\textbf {R} [dt-005E]

An endofunctor \mathcal {F} is cocontinuous iff it preserves colimits of \omega -chains of cpos. That is, given a chain where A is a colimit:

Then \mathcal {F}(A) is a colimit for the following chain: