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A compact object (mathematics) is an object whose represented Hom functor preserves filtered colimits. This preservation condition differs from the extra right-adjoint property defining a tiny object.

An object $A$ of a Cartesian closed category is tiny when exponentiation $(-{)}^A$ itself has a right adjoint.

The extra adjunction defining a tiny object should not be confused with the filtered-colimit condition for a compact object (mathematics).