Page "Limit (category theory)" Paragraph 12

Limits are also referred to as universal cones, since they are characterized by a universal property ( see below for more information ).

As with every universal property, the above definition describes a balanced state of generality: The limit object L has to be general enough to allow any other cone to factor through it ; on the other hand, L has to be sufficiently specific, so that only one such factorization is possible for every cone.