natural numbers object (English, noun)
expansion: natural numbers object (plural natural numbers objects)
Senses:
topics: category-theory
computing
engineering
mathematics
natural-sciences
physical-sciences
sciences
glosses: 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., sⁿ∘z) yields other global elements of the same object which correspond to the natural numbers (sⁿ∘z↔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') and which commutes with s; i.e., ϕ∘s=s'∘ϕ.
Forms:
form: natural numbers objects
tags: plural