How to pronounce “natural numbers object”

Meaning

• [Noun]
• (category theory) An object which has a distinguished global element (which may be called z, for “zero”) and a distinguished endomorphism (which may be called s, for “successor”) such that iterated compositions of s upon z (i.e.,
• s
• n
• ∘
• z
• {\displaystyle s^{n}\circ z}
• ) yields other global elements of the same object which correspond to the natural numbers (
• s
• n
• ∘
• z
• ↔
• n
• {\displaystyle s^{n}\circ z\leftrightarrow n}
• ). Such object has the universal property that for any other object with a distinguished global element (call it z’) and a distinguished endomorphism (call it s’), there is a unique morphism (call it φ) from the given object to the other object which maps z to z’ (
• ϕ
• ∘
• z
• =
• z
• ′
• {\displaystyle \phi \circ z=z'}
• ) and which commutes with s; i.e.,
• ϕ
• ∘
• s
• =
• s
• ′
• ∘
• ϕ
• {\displaystyle \phi \circ s=s'\circ \phi }
• .

Practice Nearby Words

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Similar Sounds

natural numbers, natural number, naturalism, natural spring, natural resin, whole numbers, mission impossible, magic number, serial number, square numbers