The traditionalist view is that the “between” should only be used if there are only two objects to compare; and “among” or “amongst” should be used for more than two objects. Most style guides and dictionaries do not support this advice and say that “between” can be used to refer to something that is in time, space, or the interval that separates more than two elements. M-W says the idea of being able to be used only between two elements is “tenacious but unfounded,” and AHD4 calls it a “widespread but unjustified tradition.” The OED says, “In all respects, it was extended to more than two between its first appearance.” Chambers says, “It is acceptable to use `between` in relation to more than two people or things,” although it is said that `under` may be more appropriate in certain circumstances. We use among to suggest a feeling of being part of something else or being surrounded or locked in something else. It typically follows a plural substantive sentence: Between you and me, between you and him, etc., are false; between the two, only the objective case should follow: between you and me, between you and him, etc. His money was divided between his son and daughter. Relationships: The Chicago Manual of Style describes them as one-for-one relationships. Sometimes they are between two objects, groups or people, as in these sentences: “The agreement was concluded between the seller, the buyer and the guarantor.” Flights between London and Crete will start in early April. The idea to use between two alternatives and less than two is a zombie rule with a family tree. It was invented in 1851 by Goold Brown in his Grammars d`Anglais to demonstrate its superiority over the ancient grammarians who had “abused” between more than two alternatives. UK agreement that information disclosed at a meeting can be used, but not the identities of the participants or organisations to which they belong If exactly two entities are indicated, it is always necessary to use between: “This contract is between the seller and the buyer.” The difference between these results is not statistically significant. (correct)✓ From this context, you have been correct in your use of between.
“Cook and. al.” was part of a certain group of individuals, so you would use each other….