Function composition

Function composition is an algebraic notion which DiSciullo &amp; Williams (1987) adopt from Categorial Grammar to account for an important difference between compounding and affixation. In compounding the non-head satisfies a theta-role of the head. The non-head of a complex word headed by an affix, however, does not satisfy a theta-role of the affix; rather the affix and the stem form a composed argument structure. In order to be able to relate the argument structure of an affixal head to its non-head, they propose that suffixes are functors with respect to their complements.

Example
The English adjective complete has a Theme as its the external argument, and the nominal suffix -ness the "degree" argument R, as in (i). Since -ness is assumed to be a functor, function composition yields the composed argument structure in (ii):

(i) complete	-ness		=&gt;	(ii)	completeness (Th)	(R)				((Th) R) 		functor

Link
Utrecht Lexicon of Linguistics