Co-analysis

In morphosyntax, co-analysis is a concept proposed by Williams (1979) and Di Sciullo & Williams (1987) to account for a situation where one grammatical function (e.g. possessive) is expressed syntactically as well as morphologically, i.e. by adding a grammatical element both to a phrase as a whole and to the head of that phrase.

Examples
The English possessive marker 's sometimes appears to be attached to a possessor phrase as a whole (cf. (i)), and in other cases it seems to be attached to a noun (cf. (ii)):

(i) [the man on the corner]'s hat

(ii) his hat (= [he]'s hat)

Phrases such as the one in (iii) are ambiguous, since the possessive is either attached to the NP the man or to the N man. To account for this ambiguity, Williams & Di Sciullo assign a co-analyzed structure to the NP the man's, cf. (iv):

(iii) the man's hat (= [the man]'s hat or the [man]'s hat)

(iv) NP                      /   \ NP   \ / \    \			                  the   man's hat \	|   /			                    \    N  / \	 \ /	                     \	  N                       \ / NP

Comment
Co-analysis means that a syntactic and a morphological representation are assigned to one phrase.

Link
Utrecht Lexicon of Linguistics