A nominative conjoined object (NomConjObj for short) is, first of all, a NP which is coordinate in form (consisting of two or more conjoined NPs) and which serves as an object (a direct object or prepositional object). Then, at least one of the conjuncts is visibly nominative — that is, it is a 1st or 3rd person personal pronoun in its nominative form. (Other NPs show no visible evidence of their case.) Although many combinations are attested, only two seem to be really frequent:
NP and I [e.g., “to Kim and I”]
he/she and NP [e.g., “to he and Kim”]
(You will see that both serial position and person/number features are relevant.)
[Clearly, “nominative conjoined object” is an imperfect name, but it’s hard to imagine how to pack all the relevant information into a reasonably short name. And anyway, labels are not definitions.]
The full set of facts about pronoun case in English ranges over quite a bit of territory, including, most notably, AccConjSubjs, as in “Me and Kim went swimming”. The advice literature on the general topic is vast, and I won’t attempt to survey it here, though I point out that MWDEU has an excellent entry (between you and I) on NomConjObjs.
On to some references on NomConjObjs.
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