  As Eilenberg &amp; Mac Lane promptly remark, objects play a secondary role and could be entirely omitted from the definition. Doing so, however, would make the manipulation of the applications less convenient. It is practically suitable, and perhaps psychologically more simple to think in terms of mappings and objects. The term “aggregate” is used by Eilenberg &amp; Mac Lane themselves, presumably so as to remain neutral with respect to the background set theory one wants to adopt.