The universal property of limits is a foundational concept in category theory that defines how limits can be uniquely characterized by their universal mapping properties. It establishes that for any cone over a diagram, there exists a unique morphism from the cone's apex to the limit, making limits a way to 'capture' all the information of a diagram in a single object. This property plays a crucial role in understanding derived functors, as it links the concept of limits with their ability to create new mathematical structures through functorial operations.
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