• 門もん — gate
• 校門こうもん — school gate
• 門番もんばん — gatekeeper
• 門前もんぜん — in front of a gate (often a temple gate)
• 門戸もんこ — gateway / door (often metaphorical)
• 入門にゅうもん — introduction / beginner’s guide
• 部門ぶもん — department / division
• 名門めいもん — prestigious school / family
• 専門せんもん — specialty / field of study
• 門松かどまつ — New Year’s pine decoration

門 originally pictures a physical gate — a clear boundary and point of entry. In modern Japanese it also appears in words for “departments,” “schools,” and “fields,” extending the idea of a “gateway” into a new area of knowledge.