Cohortative mood

The hortative (ⁱ/ˈhɔːrtətɪv/; abbreviated HORT) is a group of semantically similar deontic modalities in some languages. Hortative modalities encourage or urge. In English, there are seven hortative modalities: the adhortative, exhortative, suprahortative, cohortative, dehortative, inhortative, and infrahortative. They differ by intensity, attitude (for or against), and—in the case of the cohortative—person.

Hortative modalities signal the speaker's encouragement or discouragement toward the addressee's bringing about the proposition of an utterance. For this reason, hortative constructions can be used only in the first-person plural (cohortative) and second-person singular and plural (adhortative, exhortative, dehortative, and inhortative).

The term hortative dates to 1576, from Late Latin hortatorius "encouraging, cheering", from hortatus, past participle of hortari "exhort, encourage", intensive of horiri "urge, incite, encourage".

Hortative modality is often mistaken for other modalities due to semantic or lexical similarities. Hortative constructions also rarely have forms that are uniquely hortative. Let's (let us in its contracted form) is an exception to this. However, even let's in its long form let us as well as the colloquial semantic equal leave us may be used as cohortatives as well as for other functions.

...
Wikipedia