We do not, in general, require that this collection be small; if it is so we would call it a “small sink”.
The dual concept is a collection of morphisms of whose sources (domains) are all :
Confusingly, this dual concept is called a source from in , even though the term ‘source’ has another meaning, one which we just used in the definition! One can of course say ‘domain’ instead of ‘source’ for this other meaning, but that leads to other confusions. Or one can say ‘cosink’ for a source in the sense dual to a sink, since a source from in is the same as a sink to in the opposite category .
If is a functor, then a -structured sink is a collection of objects together with a sink in of the form . This notion figures in the definition of a final lift.