Where does “monastery” come from?

I need to analyze this etymology chain carefully. Looking at the chain provided: - Old French monastere - Latin monasterium - Ancient Greek μοναστήριον - Ancient Greek μόνος (meaning "alone/single") - Ancient Greek χρῶμα - Proto-Indo-European gʰreu - Ancient Greek χρῶμα - Proto-Indo-European gʰreu There's a significant problem here: the chain appears corrupted or illogical. The sequence jumps from μόνος (alone) to χρῶμα (color), then to PIE gʰreu, then repeats. This doesn't form a coherent etymological path. Typically, "monastery" comes from Greek μοναστήριον, derived from μόνος (alone), referring to a place where solitary monks live. Given the instruction

monastery (English): Building for housing monks or others who have...