Abstract :
A natural numbers object image in a cartesian closed category associates to each pair of arrows a:1→A and h:A→A a unique arrow f:N→A such that f0=a and fS=hf. We call (N,0,S) a quasi-natural numbers object if the arrow f is unique only up to quasi-equality, where two arrows N→A are called quasi-equal if they are equalized by the canonical arrow A→N(NA). We show that quasi-natural numbers objects can be characterized equationally.
