universal property

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The exponential object ZY defined with the universal property that (ZY, eval) is the terminal object of the comma category (–×Y↓Z).


universal property (plural universal properties)

  1. (mathematics) A definition of a mathematical object, up to isomorphism, in terms of abstract maps between it and other objects of the same category. More specifically, it is either the initial property of an initial object in a coslice-like comma category or the terminal property of a terminal object in a slice-like comma category; these are roughly analogous to the minimum and the maximum (respectively) of a certain lattice, and are used to define the object uniquely up to isomorphism.