An equational variant of Lawvere's natural numbers object

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• 作者：Lambek ; J.
• 关键词：18C99 ; 18D99
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2000
• 期刊代码：35_00224049
• 类别：mt
• 出版时间：December 1, 2000
• 卷：154
• 期：1-3
• 页码：265-272
• 文件大小：77.0 K

摘要

A natural numbers object Cannot display formula 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.