ḱey-
“to lie down, home, bed”settle, home, beloved
Root for lying/settling, yielding Latin civis (citizen), English home, cemetery.
Discussion
The PIE root *ḱey- (to lie down, to settle, to be at rest — extended to "home, bed, beloved place") produced the vocabulary of domestic settlement and the state of being at home — a word family that connects the physical act of lying down with the social institution of the household.
Latin cīvis (citizen — originally "one who lies down/settles in a place," a member of a settled community) gave English: civic (pertaining to citizens), civil (pertaining to citizens — then refined, polite, as citizens should be), civilise (to make into a citizen-community), civilisation (the state of being citizen-organised), and city (from Latin civitās, the body of citizens). The entire Western vocabulary of urban life and political organisation rests on a PIE root for lying down: a citizen is, etymologically, one who has settled.
Greek keîmai (κεῖμαι, "I lie, I am placed, I rest") preserves the physical posture sense. The derivative koimḗtērion (κοιμητήριον, "a sleeping place") gave English cemetery — literally "a place for lying down," a dormitory for the dead. The euphemism is ancient and deliberate: the dead are not gone but sleeping.
Sanskrit śáye ("he lies down") and the related śivá- ("auspicious, benign" — possibly from the domestic comfort of the settled home) continue the Indo-Iranian reflex.
Old English hām (home) may be connected through a related root or extension — the home as "the place where one lies down." German Heim (home) and the English combining form -ham in place names (Birmingham, Nottingham — originally homesteads) may share this PIE ancestry.
The root's arc from "lying down" to "citizen" encodes the origin of civilisation itself: to be civilised is to have settled, to have stopped moving and lain down in one place. The nomad becomes a citizen by the act of *ḱey- — by lying down and staying.
Notes
Pokorny 539-540. English civic, city, cemetery, hamlet.