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Agreement refers to requirement (in a language's grammar) of words to match certain others in some property.
For example, "I are" does not agree in person.
Agreement introduces dependencies (in that sentences with the same structure may need changing in various places if you change some aspect of it), and often some information redundancy as well. It interacts with semantics and can be used to add information, and reduce potentially ambiguous interpretations, for example settling what number a noun is in, to aid to disambiguation and aid finding referents.
Agreement rules are not always basic. Consider, for example, genderless pronouns compared to gendered pronouns. You probably do it automatically in your native language, but try to describe it in detail.
Requirements depend for a good part on how inflected a language is. For example, modern English has fewer cases than it used to, so its agreement rules are also less complex.
Agreement isn't always strictly enforced. Things like morphologized forms,
English does not mark (that is, inflect for) much agreement, nor impose it as some other, more inflected Indo-European languages.
- verbs generally must agree with objects in person and number. For example, it is "monkeys eat my brain" but "a monkey eats my brain."