Derived cotriples

Suppose (G,\epsilon,\delta) is a cotriple on a complete category. Let G^2 ===> G ---> G' be a coequalizer. Then we can find canonical (perhaps unique) \epsilon': G' ---> Id and \delta': G' ---> G'^2 such that (G',\epsilon',\delta') is a new cotriple on the category and such that G ---> G' is a map of cotriples. It seems reasonable to call this the derived cotriple. This process can be repeated, apparently forever, using colimits at limit ordinals. If it ever stablizes, the resultant cotriple will be idempotent and vice versa. Does any know whether this construction has been studied before? Michael -- The United States has the best congress money can buy. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]