A universal cocone is a specific type of cocone in category theory that provides a way to describe the relationships between objects and morphisms in a diagram. It consists of a cone with a unique morphism from any object in the diagram to the cocone, allowing for a universal property to hold, meaning it can uniquely factor through other cocones. This concept is closely linked to colimits and terminal objects, serving as a bridge to understand how objects can be constructed and related through categorical limits.
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