Definition. Terminal Object

2025-02-07 ยท nLab ยท category-theory universal-property

An object ๐‘ in a category ๐’ž๏ธ€ is terminal if there is a unique morphism from any other object into it.

Because terminal objects are unique up to unique isomorphism (as are all universal objects) we often just write โŠค to refer to the terminal object. Likewise, !:๐‘‘โ†’โŠค refers to the unique morphism into โŠค.

terminal-object definition entries/category/terminal-object.hel